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|
|
|
|
| 2010-03-11 |
Thu |
John Aston (Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks I19 |
Using Functional Principal Component Analysis and Mixed Effect Models to Analyse Spoken Language |
| |
| |
Abstract:
Fundamental frequency (F0, broadly "pitch") is an integral part of spoken human language; however, a comprehensive quantitative model for F0 can be a challenge to formulate due to the large number of effects and interactions between effects that lie behind the human voice's production of F0, and the very nature of the data being a contour rather than a point. A semi-parametric functional response model for F0 will be formulated by incorporating linear mixed effects models through the functional principal component scores. This model is applied to the problem of modelling F0 in the tone languages such as Mandarin and Qiang (a dialect from China), languages in which relative pitch information is part of each word's dictionary entry.
|
|
| 2010-03-04 |
Thu |
Jonty Rougier (Bristol) |
Probability and Statistics Seminar |
| 14:00 |
Hicks K14 |
Uncertainty and Risk in Natural Hazards |
| |
| |
Abstract:
In natural hazards (volcanoes, earthquakes, floods etc) it is useful for
modelling purposes to make a distinction between aleatory and epistemic
uncertainty, where the former represents the inherent or natural
uncertainty of the hazard, and the latter represents everything else.
Natural hazards scientists are often reluctant to quantify epistemic
uncertainty with probability, due in a large part to its subjective
nature. But this challenge should be weighed against the additional
problems that non-quantified uncertainty create for the risk manager and
the policymaker. This talk explores these issues in the light of the
recent NERC scoping study on natural hazards uncertainty and risk.
|
|
| 2010-02-25 |
Thu |
Mark Broom (Sussex) |
Probability and Statistics Seminar |
| 14:00 |
Hicks I19 |
Models of evolution on structured populations with asymmetry
|
| |
| |
Abstract:
We investigate two examples of models of populations with structure, involving asymmetry. These are different in character, with the common theme that both the structure and the asymmetry have an important influence on population outcomes. The first part of the talk concerns the study of evolutionary dynamics on populations with some non-homogeneous structure, a topic in which there is a rapidly growing interest. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. This process is a Markov chain and we prove several mathematical results. For example we prove that for all but a restricted set of graphs, (almost) all states are accessible from the possible initial states. To find the fixation probability of a line graph we relate this to a two-dimensional random walk which is not spatially homogeneous. We investigate our solutions numerically and find that for mutants with fitness greater than the resident, the existence of an asymmetric population structure helps the spread of the mutants. Thus it may be that models assuming well-mixed populations consistently underestimate the rate of evolutionary change.
In the second part we consider a model of kleptoparasitism, the stealing of food from one animal by another. The handling process of food items can take some time and the value of such items can vary depending upon how much handling an item has received. Furthermore this information may be known to the handler but not the potential challenger, so there is an asymmetry between the information possessed by the two competitors. We use game-theoretic methods to investigate the consequences of this asymmetry for continuously consumed food items, depending upon various natural parameters. A variety of solutions are found, and there are complex situations where three possible solutions can occur for the same set of parameters. It is also possible to have situations which involve members of the population exhibiting different behaviours from each other. We find that the asymmetry of information often appears to favour the challenger, despite the fact that it possesses less information than the challenged individual.
|
|
| 2010-02-22 |
Mon |
Tom Sutherland (Sheffield) |
Quantisation |
| 16:10 |
J11 |
Deformation quantisation
|
| |
| |
Abstract:
Deformation quantisation (or phase-space quantisation) comes from the idea of
constructing a representation of quantum mechanics by deforming the commutative
product in the algebra of functions on a Poisson manifold to a non-commutative
so-called star-product. It first appeared in the work of Dirac, and over the
years many different authors have proved that deformation quantisations exist
for successively broader classes of manifolds.
The case of a general Poisson manifold was finally proved by Kontsevich who
showed that it was implied by his Formality Conjecture. This talk will focus
on giving an outline of his proof.
|
|
| 2010-02-18 |
Thu |
Vincent Macaulay (Glasgow) |
Probability and Statistics Seminar |
| 14:00 |
Hicks K14 |
Inference about past human migration episodes from modern DNA data |
| |
| |
Abstract:
One view of human prehistory is of a set of punctuated migration events
across space and time, associated with settlement, resettlement and
discrete phases of immigration. It is pertinent to ask whether the
variability that exists in the DNA sequences of samples of people living
now, something which can be relatively easily measured, can be used to
fit and test such models. Population genetics theory already makes
predictions of patterns of genetic variation under certain very simple
models of prehistoric demography. In this presentation I will describe
an alternative, but still quite simple, model designed to capture more
aspects of human prehistory of interest to the archaeologist, show how
it can be rephrased as a mixture model, and illustrate the kinds of
inferences that can be made on a real data set, taking a Bayesian
approach.
|
|
| 2010-02-11 |
Thu |
Jonathan Jordan (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks K14 |
Geometric preferential attachment graphs
|
| |
| |
Abstract:
Preferential attachment (or ßcale-free") random graphs, in which a growing network develops by new vertices attaching preferentially to existing vertices which already have a high degree, were proposed, originally by Barabási and Albert, as models for networks appearing in a wide range of contexts (including biological, technological and social) in which examination of data often reveals an approximately power law distribution of vertex degrees. It was rigorously shown by Bollobás at al that preferential attachment graphs did indeed have this property.
In many of the contexts in which random graph models are used it makes sense for the vertices to have some location in space. The original preferential attachment model has no spatial element, and in this talk I will describe a model which combines a preferential attachment element with a spatial element. I will describe results which show that under certain conditions on the spatial element the power law degree property is retained.
I intend that most of the talk should be accessible to an applied audience, though there will be a few slides discussing my proof method.
|
|
| 2010-01-28 |
Thu |
David Wishart (St Andrews) |
RSS Seminar Series |
| 16:30 |
Hicks Room K14 |
The Flavour of Whisky: A statistical and hedonistic appraisal, with Robert Burns |
|
| 2009-12-17 |
Thu |
Ben Youngman (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Modelling phenomena using different data sources
|
| |
| |
Abstract:
The building of structures requires that their strength be sufficient to withstand day-to-day wear and tear but also, ideally, all levels of extreme punishment. Yet in practice economical grounds require that some trade-off between strength and susceptibility to damage be made to avoid costs spiralling. As it is logical to expect that the largest events will be most damaging, there is therefore motivation to estimate the distribution of extremes by, for example, estimating the probability of exceeding a certain high level. This is a typical problem in extremal analyses. More recently this problem has been extended by seeking estimates of extremal distributions over space, which is the topic of this talk, though here matters will be further complicated by spatio-temporally sparse data. To try to combat this, data obtained via different methods, yet in theory quantifying the same phenomenon, will be modelled simultaneously. Extreme value theory will be drawn upon to tackle this problem. This talk begins with an introduction to the topic and progresses by applying some ideas discussed.
|
|
| 2009-12-17 |
Thu |
Afzalina Azmee (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Two-stage testing in three-arm non-inferiority trials |
| |
| |
Abstract:
The aim of a non-inferiority trial is to show that the new experimental treatment is not worse than the reference treatment by more than a certain, pre-defined margin. We consider the design of a 3-arm non-inferiority trial, where the inclusion of a placebo group is permissible. The widely used 3-arm non-inferiority procedure was authoritatively first described by Pigeot et al. (2003), which involved establishing superiority of reference against placebo in the first stage before testing non-inferiority of experimental against reference in the second stage. If this preliminary test fails, the second-stage test has to be abandoned. In such an eventuality, we believe the whole study will be wasted as nothing new could be learnt about the new experimental treatment. Therefore, instead of showing superiority in the first stage, we propose that the reference treatment has to be significantly different than placebo as a pre-requisite before using Fieller’s confidence interval to assess non-inferiority. This procedure leads to no peculiar intervals (i.e. exclusive or imaginary) and offers easy interpretation regarding the efficacy of experimental and reference treatments.
|
|
| 2009-12-10 |
Thu |
Lesley Morrell (Leeds) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Modelling the Selfish Herd: Behavioural mechanisms for aggregation in animals |
| |
| |
Abstract:
The theory of the selfish herd (WD Hamilton, 1971) has been highly influential to our understanding of animal aggregation. Hamilton proposed that in order to reduce its risk of predation, an individual should approach its nearest neighbour, reducing its risk at the expense of those around it. Despite extensive empirical support, the selfish herd hypothesis has been criticized on theoretical grounds: approaching the nearest neighbour does not result in the observed dense aggregations, and the nearest neighbour in space is not necessarily the one that can be reached fastest. To combat these problems, increasingly complex movement rules have been proposed, successfully producing dense aggregations of individuals, yet various questions remain unanswered. Is one movement rule always the most successful? How to ecological parameters such as the size and density of the group affect rule success? Is the behaviour of the predator important? Should all individuals within a group use the same rule, or should they adjust their behaviour based on where in the group they are, or in response to the behaviour of others? We use simulation models of animal groups to investigate these questions, and demonstrate that there is no rule that performs best under all circumstances: the ecology of the predator and prey are both key in determining how animals should respond to a predation attempt.
|
|
| 2009-12-07 |
Mon |
Elizabeth Winstanley (Sheffield) |
Quantisation |
| 16:10 |
J11 |
Quantisation and Physics |
|
| 2009-12-03 |
Thu |
David Percy (Salford) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Predictive elicitation of subjective prior distributions
|
| |
| |
Abstract:
This seminar tackles the problem of specifying subjective prior
distributions for unknown model parameters. We first review strategies
for selecting families of priors for common models, including univariate
and multivariate probability distributions, generalized linear models
and stochastic processes. We then consider methods for evaluating the
hyperparameters of these prior distributions.
Specifically, we focus on predictive elicitation using quantiles and
cumulative probabilities, illustrating the natural beauty and
philosophical benefits of this approach. We discuss problems relating to
inherent constraints and computational difficulties, and conclude that
some compromise is necessary. We illustrate the technique in
applications from sport, medicine and industry.
|
|
| 2009-11-30 |
Mon |
Dave Applebaum (Sheffield) |
Quantisation |
| 16:10 |
J11 |
Mysteries and functors (part 2)
|
|
| 2009-11-26 |
Thu |
David Sexton (The Met Office) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Making probabilistic climate projections for the UK
|
| |
| |
Abstract:
UKCP09, the latest set of climate projections for the UK were released
on June
18th 2009. For the first time the climate projections for the UK are
probabilistic, so that it is an appropriate tool for people who are
taking a
risk-based approach to policy and decision making. I will describe how
the
probabilities were estimated using a) a combination of a number of
climate
model ensembles which explore parameter uncertainty in different
components
of the Earth System b) a set of international climate models other than
the
Met Office Hadley Centre model and c) a Bayesian framework which
combines this
climate model output with observations to provide probabilities that are
relevant
to the real world and therefore relevant to risk-based decision making.
I will also outline the main areas of the production system that could
benefit
from further research into statistical methods and better experimental
design.
|
|
| 2009-11-25 |
Wed |
Kostas Triantafyllopoulos (Sheffield) |
AM/P+S Colloquium |
| 16:00 |
LT A |
Bayesian methods for flexible manoeuvring systems in control |
| |
| |
Abstract:
This talk serves as an Interim Report of the BtG grant on a Flagship project between the Departments of Probability and Statistics, Applied Mathematics and Automatic Control and Systems Engineering. This project investigates the application of Bayesian statistical modelling to a class of problems in control, and in particular to the system modelling and tracking control of a twin rotor multi-input multi-output system (TRMS) in hovering mode. Systematic stochastic modelling of the hovering property of the helicopter/TRMS is vital for a variety of flight missions including load delivery and air-sea rescue.
We describe parametric and non-parametric models (forward and inverse), with the aid of which we empirically explore the non-minimum phase phenomenon of the non-linear system. The parametric model is a linear Bayesian time series model which shares some resemblance to the celebrated Kalman filter, and the non-parametric model is a Neural Network (NN) model. We discuss in detail the Bayesian model and provide a comparative analysis with the NN model, in relation to non-minimum phase behaviour. We provide some discussion on future directions of modelling, in particular in the view of (a) establishing non-minimum phase behaviour of the models theoretically and (b) proposing other non-parametric statistical modelling approaches. Finally, we showcase the application of Bayesian statistics in signal processing and in control, something that has not been explored / developed in the literature.
|
|
| 2009-11-23 |
Mon |
Dave Applebaum (Sheffield) |
Quantisation |
| 16:10 |
J11 |
On mysteries and functors (part 1)
|
| |
| |
Abstract:
Don't expect much category theory (even lower order). The title is based on a quote from Ed Nelson:
"First quantisation is a mystery, second quantisation is a functor,"
|
|
| 2009-11-19 |
Thu |
Mark Dixon (ATASS Ltd Exeter) |
RSS Seminar Series |
| 16:30 |
HIcks LT4 |
Statistical Modelling of Sports
|
| |
| |
Abstract:
Sports events provide a rich source of statistical modelling problems
that can be used to trade on betting exchanges such as Betfair. These
exchanges work in a very similar manner to standard financial markets,
and traders require sophisticated models based upon a detailed
knowledge of the sport in question. The aim of these models is to
provide an accurate assessment of the probability of different match
outcomes that can be compared with the "market view" to determine
whether or not to trade and, if so, at what price. In this talk we
provide a general overview of the sports betting markets and discuss
some of the statistical challenges they provide.
|
|
| 2009-11-17 |
Tue |
Eugenia Cheng (Sheffield) |
SoMaS Colloquium |
| 17:00 |
tbd |
2-vector spaces: an introduction to higher-dimensional category theory |
| |
| |
Abstract:
What is a 2-vector space, and how is it different from a 2-dimensional vector space? Why would anyone want to come up with such a notion? And once we have come up with such a notion, how do we know it deserves to be called a"2-vector space"? In this talk we will show how to answer all these questions using category theory. This example highlights one of the ways that category theory can help in mathematics: it helps us give good generalisations of structures that appear in various branches of mathematics including homotopy theory, stacks, topological quantum field theory, type theory, representation theory and concurrency theory.
This talk will be introductory; in particular it should not be necessary to be familiar with any category theory, and I will encourage Level 4 undergraduate students to attend. It will help to know what an ordinary vector space is.
|
|
| 2009-11-16 |
Mon |
David Jordan (Sheffield) |
Quantisation |
| 16:10 |
J11 |
Poisson Algebras
|
|
| 2009-11-12 |
Thu |
Vassili Kolokoltsov (Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
SDEs driven by nonlinear Levy noise with application to the construction of Markov processes with a given generator
|
|
| 2009-11-09 |
Mon |
Paul Mitchener (Sheffield) |
Quantisation |
| 16:10 |
J11 |
C*-algebraic deformation quantisation. |
|
| 2009-11-05 |
Thu |
Stanislav Volkov (Bristol) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
The simple harmonic urn
|
| |
| |
Abstract:
The simple harmonic urn is a discrete-time stochastic process on Z2
approximating the phase portrait of the harmonic oscillator using very basic
transitional probabilities on the lattice, incidentally related to the Eulerian
numbers.
This urn which we consider can be viewed as a two-colour generalized Polya urn
with negative-positive reinforcements, and in a sense it can be viewed as a
"marriage" between the Friedman urn and the OK Corral model, where we restart
the process each time it hits the horizontal axes by switching the colours of
the balls. We show the transience of the process using various couplings with
birth and death processes and renewal processes. It turns out that the simple
harmonic urn is just barely transient, as a minor modification of the model
makes it recurrent.
We also show links between this model and oriented percolation, as well as some
other interesting processes.
This is joint work with Edward Crane, Nicholas Georgiou, Rob Waters and Andrew
Wade.
|
|
| 2009-11-02 |
Mon |
Paul Mitchener (Sheffield) |
Quantisation |
| 16:10 |
J11 |
C*-algebras, states, and first steps towards C*-algebraic quantisation
|
|
| 2009-10-29 |
Thu |
Jianxin Pan (Manchester) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Modelling of Mean-Covariance Structures for Longitudinal Data
|
| |
| |
Abstract:
It is well known that when analysing longitudinal data, misspecification of covariance structures may lead to very inefficient or even biased estimators
of parameters in the mean structure. Covariance structures, like the mean,
can be modelled using linear or nonlinear regression models techniques.
Various estimation methods have been recently developed for modelling of
mean and covariance structures, simultaneously. In this talk, I will introduce
such methods on modelling of mean-covariance structures for longitudinal data, including linear and non-linear regression models, variable selection, semiparametric models, etc. Real examples and simulation studies will be presented for illustration.
|
|
| 2009-10-26 |
Mon |
Kirill Mackenzie (Sheffield) |
Quantisation |
| 16:00 |
J11 |
Poisson Manifolds (part 2) |
|
| 2009-10-22 |
Thu |
Tim Heaton (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Reconstructing a Wiener process from observations at imprecise
times: Bayesian radiocarbon calibration |
| |
| |
Abstract:
For accurate radiocarbon dating, it is necessary to identify fluctuations in the level
of radioactive carbon 14C present in the atmosphere through time. The processes
underlying these variations are not understood and so a data-based calibration curve
is required.
In this talk we present a novel MCMC approach to the production of the inter-
nationally agreed curve and the individual challenges involved. Our methodology
models the calibration data as noisy observations of a Wiener process and updates
sample paths through use of a Metropolis-within-Gibbs algorithm.
Implementation of this algorithm is complicated by certain specific features of the
data used, namely that many data points:
• relate to the mean of the Wiener process over a period of time rather than at
a specific point,
• have calendar dates found using methods (e.g. Uranium-Thorium) which are
themselves uncertain,
• have ordering constraints and correlations in their calendar date uncertainty
- for example data are sampled along the same core or have floating calendar
dates matched to another sample for which the calendar age is more accurately
known.
We give an overview of these issues and discuss their implications for the resulting
sampler.
|
|
| 2009-10-19 |
Mon |
Kirill Mackenzie (Sheffield) |
Quantisation |
| 16:00 |
J11 |
Poisson Manifolds (part 1) |
| |
| |
Abstract:
Here is a sketch of what I propose for the lectures on Poisson manifolds.
+ Linear Poisson structures from Lie algebras
+ Tangent bundles are like Lie algebras ...
+ Symplectic structures and the Poisson bracket
+ Reduction of a Hamiltonian action leads to a Poisson manifold
+ Formalisms for working with Poisson structures: bracket of functions,
bracket of 1-forms, Schouten bracket.
+ The symplectic leaves of a Poisson manifold
+ The `pre-Kontsevich approach' to quantization: Symplectic realizations.
Sketch of integrability.
I'm assuming familiarity with manifolds and tangent and cotangent bundles,
and differential forms. For Lie algebras and Lie groups nothing at a deep level is required.
|
|
| 2009-10-15 |
Thu |
M. Eileen Magnello (University College London) |
RSS Seminar Series |
| 16:30 |
Hicks Room K14 |
The Development of the Provincial Statistical Societies and the Statistical Society of London |
| |
| |
Abstract:
The statistical societies that emerged in the 1830s were largely a response to the massive social and technological changes that occurred in early- and mid-Victorian Britain. Transportation and communication underpinned these changes: the railways made it possible to travel to the many academic societies across Britain, whilst the penny post, the telegraph and the steam press created a communications revolution, which led to the proliferation of statistical publications. Concomitant with these developments were methodological changes in statistics and the emergence of a new statistical language for the Victorians who were passionate about documenting these social changes in Britain. This paper will examine how the modernisation of Britain led to the growth of a statistical movement in Britain, which, in turn, helped to establish statistical societies and publications in the provinces and London.
|
|
| 2009-10-12 |
Mon |
Paul Mitchener (Sheffield) |
Quantisation |
| 16:00 |
J11 |
Introduction to C∗-algebras |
| |
| |
Abstract:
This talk is intended to be extremely elementary, introducing C∗-algebras and looking at some fundamental properties. We assume no know knowledge of analysis beyond the definitions of a normed vector space and completeness.
|
|
| 2009-10-08 |
Thu |
Nathan Green (Dstl Porton Down) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Determining the Source of a Hazardous Atmospheric Release
|
| |
| |
Abstract:
A methodology is explored for making inference about parameters of a
hazardous atmospheric release from sensor readings. The key difficulty
in performing this inference is that the results must be obtained in a
very short timescale (5 min) to make use of the inference for
protection. The methodology that has been developed uses some of the
components in a sequential Monte Carlo algorithm. However, this
inference problem is different from many other sequential Monte Carlo
problems, in that there are no state evolution equations, the forward
model is highly non-linear and the likelihoods are non-Gaussian.
Results for inferences made of atmospheric releases (both real and
simulated) of material will be presented, demonstrating that the
sampling scheme performs adequately despite constraints of a short time
span for calculations. Potential future developments and issues will
also be discussed to show areas of future research interest.
|
|
| 2009-10-07 |
Wed |
Prof Michael Berry FRS (Bristol) |
|
| 16:00 |
J11 |
Two by two
|
| |
| |
Abstract:
A tutorial account of families of 2x2 matrices labelled by several parameters will concentrate on the neighbourhood of degeneracies. The emphasis will be on the differences between hermitian and nonhermitian matrices, considered geometric. Physical phenomena in optics and atomic physics where such degeneracies play a crucial role will be described.
This introductory talk by Prof Berry will serves to launch the MAGIC courses for 2009/10.
|
|
| 2009-10-01 |
Thu |
Jeremy Oakley (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT6 |
Eliciting Probability Distributions
|
| |
| |
Abstract:
Elicitation is the process of extracting expert knowledge about some unknown
quantity of interest and representing that knowledge with a suitable
probability distribution. It is an important component of Bayesian inference,
risk analysis, and decision-making in the presence of uncertainty. In this talk
I will give an introduction to the field and discuss some current research
interests, including nonparametric elicitation, the trial roulette method, and
SHELF: the Sheffield Elicitation Framework.
|
|
| 2009-09-03 |
Thu |
Tom Leinster (Glasgow (visiting Sheffield)) |
|
| 15:00 |
J11 |
Quantifying Biodiversity III
|
| |
| |
Abstract:
There is a lively and chaotic literature on how to quantify
the diversity of a biological community. The challenge is to take a
big mass of data about a community and distill it down to a single
number, measuring its `diversity'. People have been arguing about how
to do it for decades.
In my talks I hope to shed some light on the matter. This involves
various new pieces of mathematics: some newish category theory, a new
invariant of metric spaces, and some new aspects of the notion of
entropy. The emphasis these get in the talks will depend entirely on
the audience; rest assured that I'll explain whatever's necessary.
For better or worse, I'll entirely ignore the statistical side.
[Some people might feel that one talk is all the appreciation they can
handle. For their sake, I'll try to put the material of broadest
appeal into the first one.]
|
|
| 2009-09-02 |
Wed |
Tom Leinster (Glasgow (visiting Sheffield)) |
|
| 15:00 |
J11 |
Quantifying Biodiversity II
|
| |
| |
Abstract:
There is a lively and chaotic literature on how to quantify
the diversity of a biological community. The challenge is to take a
big mass of data about a community and distill it down to a single
number, measuring its `diversity'. People have been arguing about how
to do it for decades.
In my talks I hope to shed some light on the matter. This involves
various new pieces of mathematics: some newish category theory, a new
invariant of metric spaces, and some new aspects of the notion of
entropy. The emphasis these get in the talks will depend entirely on
the audience; rest assured that I'll explain whatever's necessary.
For better or worse, I'll entirely ignore the statistical side.
[Some people might feel that one talk is all the appreciation they can
handle. For their sake, I'll try to put the material of broadest
appeal into the first one.]
|
|
| 2009-09-01 |
Tue |
Tom Leinster (Glasgow (visiting Sheffield)) |
|
| 15:00 |
J11 |
Quantifying Biodiversity I
|
| |
| |
Abstract:
There is a lively and chaotic literature on how to quantify
the diversity of a biological community. The challenge is to take a
big mass of data about a community and distill it down to a single
number, measuring its `diversity'. People have been arguing about how
to do it for decades.
In my talks I hope to shed some light on the matter. This involves
various new pieces of mathematics: some newish category theory, a new
invariant of metric spaces, and some new aspects of the notion of
entropy. The emphasis these get in the talks will depend entirely on
the audience; rest assured that I'll explain whatever's necessary.
For better or worse, I'll entirely ignore the statistical side.
[Some people might feel that one talk is all the appreciation they can
handle. For their sake, I'll try to put the material of broadest
appeal into the first one.]
|
|
| 2009-06-04 |
Thu |
Katy Klauenberg (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Statistical Modelling for Dating Ice Cores
|
| |
| |
Abstract:
In ice cores which are drilled through ice sheets in polar regions valuable information about past environment and climate are preserved. A pivotal part of interpreting the information held within the cores is to build ice core chronologies i.e. to relate time to depth. Existing dating methods can be categorised as follows: (1) layer counting using the seasonality in signals, (2) glaciological modelling describing processes such as snow accumulation and plastic deformation of ice, (3) comparison with other dated records, or (4) any combination of these. Conventionally, implementation of these approaches does not use statistical methods.
We combine glaciological models with a Bayesian framework. For this purpose, the sources of uncertainty in the glaciological model and the knowledge about these are formalised. Additionally, we include information from layer counting and other dated records (i.e. traces from volcanic eruptions) to constrain the resulting dating. During the talk the setup of this statistical model will be described, the effect of uncertainty in the glaciological model will be demonstrated and the interplay with information from other dating methods will be illustrated.
This combined statistical dating approach is applied to date Antarctic ice cores. For the first time the effects of uncertainty implied by the dating method are investigated for ice core chronologies, which provides valueable insights for the applied community.
|
|
| 2009-05-19 |
Tue |
John Biggins (Sheffield) |
SoMaS Colloquium |
| 17:05 |
LT 6 Hicks |
Branching Out
|
| |
| |
Abstract:
I aim to give an overview of the synthesis of two classical probability
models (branching processes and random walk) and to indicate
connections with several other parts of mathematics.
|
|
| 2009-05-14 |
Thu |
Erika Hausenblas (Saltzburg) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Stochastic Partial Differential Equations driven by Poisson Random Measure
|
| |
| |
Abstract:
I will start with pointing out some examples coming from physics to motivate stochastic partial differential equations (SPDEs). Then I will briefly explain the differences in the dynamics between deterministic partial differential equations and SPDEs. After this motivation I will speak about stochastic integration in Banach spaces and point out the differences with the stochastic integral with respect to the Wiener process. Finally, I give some results concerning SPDEs drive by Poisson random measures.
|
|
| 2009-05-14 |
Thu |
Denise Lievesley (Kings College London) |
RSS Seminar Series |
| 16:30 |
Hicks LT2 |
The Statistician as Public Servant
|
| |
| |
Abstract:
Denise Lievesley will draw on her experience of working in both statistics and information services in the UK and in the United Nations to highlight the tension between relevance and statistics. But relevant for whom? Relevance should not be defined narrowly but should take account of the very varied communities of users. As statisticians we want what we produce to be used to make a difference in the quality of people's lives which means that our data must be fed into public policy. But how do we ensure that the data and associated interpretation are germane to the development of policies whilst at the same time protecting them from political interference? The challenge is to produce data which are both trusted and trustworthy.
|
|
| 2009-05-07 |
Thu |
Kevin Walters (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Are colonic stem cell data consistent with the immortal model of stem cell division under non-random strand segregation?
|
| |
| |
Abstract:
Stem cells have the potential to revolutionize modern medicine with their regenerative potential however little is known about tissue stem cell differentiation in-vivo. Technical advances in laboratory methods have started to provide data that allow us to make simple inferences about tissue stem cell behaviour. This talk will focus on a particular model of stem cell differentiation.
|
|
| 2009-04-30 |
Thu |
Svetlana Tishkovskaya (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Optimal Quantisation in Bayesian Estimation
|
| |
| |
Abstract:
I consider Bayesian estimation of a parameter of a continuous distribution when observation space is quantised. Quantisation, as method of approximating a continuous range of values by a discrete set, arises in many practical situations which include modern methods of digital information processing, data compression, and some procedures of collecting data. It is well known that quantising of observations reduces values of convex information functionals. This information loss can be diminished by selecting the optimal partition. I consider two criteria of optimal quantisation in Bayesian estimation: the criterion of Bayes risk minimum and the criterion of minimum of information loss measured using Shannon information. As alternative to optimal partitioning, which realisation is often computationally demanding, an asymptotically optimal quantisation is also considered.
|
|
| 2009-04-23 |
Thu |
Goran Peskir (Manchester) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
The British Put-Call Symmetry
|
| |
| |
Abstract:
I will review recent results/problems arising
in the British pricing mechanism. This involves optimal
stopping with non-monotone free boundaries.
|
|
| 2009-04-23 |
Thu |
Gennady Samorodnitsky (Cornell) |
Probability and Statistics Seminar |
| 15:30 |
Hicks LT7 |
The 2009 Applied Probability Trust Lecture
Large deviations for point processes based on stationary sequences with heavy tails
|
| |
| |
Abstract:
In many applications involving functional large deviations for partial
sums of stationary, but not iid, processes with heavy tails, a curious
phenomenon arises: closely grouped together large jumps coalesce together
in the limit, leading to loss of information of the order in which these
jumps arrive. In particular, many functionals of interest become
discontinuous. To overcome this problem we move from the functional large
deviations to the point-process-level large deviations. We develop the
appropriate topological framework and prove large deviations theorems for
point processes based on stationary sequences with heavy tails. We show
that these results are useful in many situations where functional large
deviations are not.
|
|
| 2009-04-02 |
Thu |
Philip Jonathan (Shell Technology Centre Thornton) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Modelling spatial and directional effects in extreme value analysis
|
| |
| |
Abstract:
The characteristics of extreme waves in storm-dominated regions vary systematically with a number of covariates, including location and storm direction. Reliable estimation of the magnitude of extreme events associated with a given return period requires incorporation of covariate effects within extreme value models. A spatio-directional extremes model will be outlined, based on a non-homogeneous Poisson model of peaks over threshold. At each location, a non-parametric estimate for extreme threshold as a function of storm direction is made. The rate of occurrences of threshold exceedences is modelled as a Poisson process. The size of threshold exceedences is modelled using a generalised Pareto form, the parameters of which vary smoothly in space, and are estimated using a roughness penalised likelihood approach using thin plate splines. The approach will be motivated and illustrated in application to estimation of structural design criteria for the Gulf of Mexico.
|
|
| 2009-03-26 |
Thu |
Simon Wilson (Trinity College Dublin) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Factor Analysis with a Mixture of Gaussian Factors, with Application to Separation of the Cosmic Microwave Background
|
| |
| |
Abstract:
Blind source separation is a technique in signal processing where the values of
'sources' are inferred from observations that are linear combinations of them.
The typical example is separating two voices (the sources) from a stereo audio
recording (each microphone picks up a combination of the two speakers' voices).
Both the sources and the matrix of linear 'mixing' coefficients may be unknown.
In statistical terms, it is an example of factor analysis, the main difference
being that the 'factors' here will have some interpretation and there may exist
useful prior information on them.
Here we describe an approach to factor analysis/source separation where the
sources are assumed to be Gaussian mixtures, which may be independent or
dependent e.g. mixtures of multivariate Gaussians. An MCMC procedure has been
developed that implements a fully Bayesian procedure e.g. it computes the
posterior distribution of sources, their Gaussian mixture parameters and the
matrix of linear coefficients from the data.
The method is applied to recovery of the cosmic microwave background (CMB),
being an example of source separation applied to image data. The CMB is one of
many sources of extraterrestrial microwave radiation and we observe a weighted
sum of these sources from the Earth at different frequencies. Its accurate
reconstruction is of great interest to astronomers and physicists since
knowledge of its properties, and in particular its anisotropies, will place
strong restrictions on current cosmological theories. From the perspective of
a Bayesian solution, this application is interesting as there is considerable
prior information about the linear coefficients and the sources. Results from
the analysis of data from the WMAP satellite will be presented, where microwave
radiation is observed at 5 frequencies and separated into sources, including the
CMB. A discussion of the many outstanding issues in this problem is also
presented.
|
|
| 2009-03-26 |
Thu |
Peter Goos (Antwerp) |
Probability and Statistics Seminar |
| 16:00 |
Hicks LT5 |
The optimal design of conjoint choice experiments
|
| |
| |
Abstract:
Stated preference data are commonly collected by means of conjoint
choice experiments or discrete choice experiments in marketing, health
economics or environmental economics. The optimal design of these
experiments is a challenging research area because of the nonlinearity
of the statistical models used to analyze the data. These models include
the conditional logit model, the mixed logit model and the nested logit
model. In this talk, I will discuss recent advances in the optimal
design for such models as well as some of the challenging computational
aspects of the optimal design search.
|
|
| 2009-03-19 |
Thu |
Jane Hutton (Warwick) |
RSS Seminar Series |
| 16:30 |
Hicks Room LT2 |
Being an expert witness
|
| |
| |
Abstract:
This talk will consider how and why a statistician might be an expert
witness. Practical aspects, such as understanding the difference between
civil and criminal cases, the meaning of 'expert' in a legal context, the
form of reports and fees will be discussed. My illustrations will mainly be
from civil, medical cases. Such cases are generally low profile, and so
provide a gentler introduction to being an expert witness that criminal
cases. Some differences between English, Irish, South Africa and USA courts
will be described. My intention is to encourage the audience to consider
acting as experts, as there is a contribution statisticians can make to the
judicial system.
|
|
| 2009-03-17 |
Tue |
Simon Willerton (Sheffield) |
SoMaS Colloquium |
| 17:10 |
LT6 |
Measuring metric spaces: short-sightedness and population diversity
|
| |
| |
Abstract:
Metric spaces can be used to represent many disparate things including shapes in space and the differences between species in a population. I will describe one way to measure the size of a metric space arrived at from pure mathematical considerations but discovered independently by ecologists. I will discuss connections with diversity measures and geometry. This is intended to be accessible to all in the School.
|
|
| 2009-03-12 |
Thu |
Gareth Roberts (Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Retrospective sampling
|
| |
| |
Abstract:
This talk will discuss a very simple idea for simulation called retrospective
sampling. The method can be applied in the context of many well-used
simulation methods such as rejection sampling and MCMC. A number of
very simple examples will be described to illustrate the ideas. As time permits,
I will give some applications, possibly including exact simulation of diffusion
paths and posterior distributions for Dirichlet mixture models.
|
|
| 2009-03-05 |
Thu |
David Leslie (Bristol) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Posterior weighted reinforcement learning with state uncertainty
|
| |
| |
Abstract:
Reinforcement learning models are, in essence, online algorithms to estimate the expected reward in each of a set of states by allocating observed rewards to states and calculating averages. Generally it is assumed that a learner can unambiguously identify the state of nature. However in any natural environment the state information is noisy, so that the learner cannot be certain about the current state of nature. Under state uncertainty it is no longer immediately obvious how to perform reinforcement learning, since the observed reward cannot be unambiguously allocated to a particular state of the environment. A new technique, posterior weighted reinforcement learning, is introduced. In this process the reinforcement learning updates are weighted according to the posterior state probabilities, calculated after observation of the reward. We show that this modified algorithm can converge to correct reward estimates, and show the procedure to be a variant of an online expectation-maximisation algorithm, allowing further analysis to be carried out.
|
|
| 2009-02-26 |
Thu |
Mike Titterington (Glasgow) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Approximate inference for latent variable models
|
| |
| |
Abstract:
Likelihood and Bayesian inference are not straightforward for latent
variable models,
of which mixture models constitute a special case.. For instance, in the
context of the
latter approach, conjugate priors are not available. The talk will
consider some
approximate methods that have been developed mainly in the
machine-learning literature
and will attempt to investigate their statistical credentials. In
particular,
so-called variational methods and the Expectation-Propagation method
will be
discussed. It will be explained that, in the Bayesian context,
variational methods
tend produce approximate posterior distributions that are located in the
right place but
are too concentrated, whereas the Expectation-Propagation approach
sometimes, but not
always, gets the degree of concentration, as measured by posterior
variance, right
as well.
|
|
| 2009-02-19 |
Thu |
Andrew Stuart (University of Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Metropolis-Hastings Methods for Sampling Random Functions
|
| |
| |
Abstract:
Many applied problems require the practitioner to obtain
information from a probability measure on functions. Examples
include signal processing, weather prediction, oceanography,
nuclear waste management and oil recovery. I will show that,
despite the wide variety of physical phenomena underlying
these examples, there is a common mathematical structure
which can be exploited in a number of ways. I will highlight
how this structure can be used to design efficient MCMC methods
to sample from the desired probability measure, generalizing
random walk and other Metropolis-Hastings methods to the
function space setting.
|
|
| 2009-02-12 |
Thu |
Lindsay Collins (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Climate variability and its effect on atmosphere/terrestrial-biosphere carbon fluxes
|
| |
| |
Abstract:
In my PhD I will study the effect of climate uncertainty and variability on vegetation carbon
dynamics. Our interest in the terrestrial biosphere lies in the carbon that is released into the
atmosphere or stored in the soil through the land vegetation. The Sheffield Dynamic Global
Vegetation Model (SDGVM) simulates the terrestrial vegetation processes (including
photosynthesis and respiration) and provides estimates of terrestrial carbon fluxes. The SDGVM is
driven by monthly climate data. The monthly data are downscaled to daily data within the SDGVM
using a weather generator so that the vegetation processes can be calculated daily. I will show how
temporal variability leads to differing carbon flux estimates. We aim to quantify the uncertainty in
the carbon flux estimates directly linked to uncertainty and variability in the climate data using
probabilistic sensitivity analysis (PSA) methods developed by Oakley and O'Hagan (2004) making
use of the GEM-SA software developed by Kennedy (2004) for working with complex models such
as the SDGVM. I will show how the form of the climate data makes the use of this software less
than straightforward and introduce methodology by which a PSA may be possible. This will
involve the characterisation of the uncertainty in the climate in terms of parameters that can be used
as input to GEM-SA rather than actual data.
|
|
| 2009-02-12 |
Thu |
Lu Zou (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks LT7 |
Multiple Imputations of Bio-Datasets
|
| |
| |
Abstract:
This presentation will start with a brief introduction to two Bio-datasets involved in my study. One inevitable issue is that many values are missing in both sets. Rather than ignoring them, imputation is considered. This talk will focus on the imputation of continuous variables which are to be used as Biomarkers in two situations: i) normal randomly missing situation and ii) a ‘File-matching’ situation. Several imputation methods are considered: for single imputation, the K-Nearest Neighbours method (KNN) and the EM-algorithm are studied; for multiple imputations, the Multiple Imputation using Additive Regression, Bootstrapping and Predictive Mean Matching (PMM) and the EM imputation combined with re-sampling methods are investigated. Based on the studies so far, the EM algorithm is relatively more suitable in my case.
|
|
| 2009-01-29 |
Thu |
Caitlin Buck (Sheffield) |
RSS Seminar Series |
| 14:00 |
Hicks Room K14 |
Quantifying uncertainty on the chronologies of palaeoclimate reconstructions from ice cores
|
| |
| |
Abstract:
Compacted snow and ice that form huge ice sheets in polar regions preserve valuable information about past environment and climate. Cores that are drilled through these ice deposits are analysed for physical and chemical properties, which reveal information about climate at the time the deposits were laid down. A pivotal part of interpreting the information held within these sequences is to build ice core chronologies i.e. to relate time to depth. Various approaches (and combinations thereof) are taken when constructing such chronologies: (1) layer counting using the seasonality in signals, (2) glaciological modelling describing processes such as snow accumulation and plastic deformation of ice, and (3) linking parameters in the ice core to other dated events or records. Conventionally, implementation of these approaches does not use statistical methods; this talk describes recent collaborative work in this area using a Bayesian model-based approach.
|
|
| 2009-01-29 |
Thu |
Marian Scott (Glasgow) |
RSS Seminar Series |
| 14:45 |
Hicks Room K14 |
Dating tools and measuring rates: essential ingredients for reconstructing past climate
|
| |
| |
Abstract:
Underpinning our ability to reconstruct past climate is our ability to measure time using 'clocks' based on the principle of radioactive decay or on counting atoms. These measurements and procedures are complex and may require sophisticated models for the measurement errors. Some examples of measurements errors and their estimation (as well as the statistical models used) from cosmogenic isotope dating using C-14, Be- 10, Al-26 and Cl-36 will be presented.
|
|
| 2009-01-29 |
Thu |
Andrew Parnell (Univerisity College Dublin) |
RSS Seminar Series |
| 16:00 |
Hicks Room K14 |
Estimating the synchroneity of past climate changes
|
| |
| |
Abstract:
Radiocarbon dating techniques allow us to estimate the timing of climatic shifts as evidenced by changes in pollen compositions. We use some recently developed Bayesian chronology models (Haslett and Parnell, 2008; Parnell et al 2008) to provide a framework to answer questions about the synchroneity of these shifts across Europe. This talk will discuss the statistical background to the chronology models as well as issues concerning the identification of a climatic 'event'.
|
|
| 2008-12-18 |
Thu |
George Streftaris (Heriot-Watt University) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Bayesian inference for stochastic epidemic models with non-exponential tolerance to infection
|
| |
| |
Abstract:
The transmission dynamics of an infectious disease during the outbreak of an epidemic can be stochastically described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance, following the so-called Sellke (1983) construction. In this talk I will present generalisations of the Sellke structure under the susceptible-exposed-infectious-removed (SEIR) class of epidemic models, and focus on a model with Weibull individual tolerance thresholds. Examples of simulated and real epidemic data are discussed, where inference is carried out using MCMC methods following a Bayesian approach to tackle the issue of the partial observation of the temporal course of the epidemic. The adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, demonstrating problems with more commonly used model checking techniques.
|
|
| 2008-12-11 |
Thu |
Jon Nicholl (University of Sheffield) |
RSS Seminar Series |
| 16:30 |
Pemberton Lecture Theatre, 2nd Floor, Regent Court |
What direction of travel? Reconfiguring emergency and urgent care
|
|
| 2008-12-04 |
Thu |
Mike Campbell (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
A statistician on a NICE appraisals committee
|
| |
| |
Abstract:
NICE stands for the National Institute for Health and Clinical Excellence. The
speaker has been on a NICE Appraisals committee for 7 years. He will describe
what the committee does and how NICE makes decisions. Much of the evidence to
NICE is statistical and a statistician is an important member of the committee.
A number of roles for a statistician will be described. One role is checking
for errors and he will describe some he has come across.
|
|
| 2008-11-27 |
Thu |
Jon Pitchford (University of York) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Is there something fishy about Lévy processes?
|
| |
| |
Abstract:
Lévy flights are loosely defined as random walks in which the step lengths are drawn from some underlying power law distribution. In biology, detecting Lévy-like behaviour is worryingly fashionable and interestingly controversial. Do Lévy flights really occur? If so, then why have they evolved? I will discuss possible answers to these questions, arguing that there may be a role for more general Lévy processes in biology and ecology. I will draw on two examples from my recent research: superspreading in epidemics, and stochastic foraging in patchy environments.
|
|
| 2008-11-20 |
Thu |
Martin Hairer (University of Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
A weak form of Harris's theorem
|
| |
| |
Abstract:
Harris' theorem gives easily verifiable conditions for a Markov operator
to have a spectral gap in a weighted supremum norm. We are going to
show a new elementary proof of this result. This proof can then be
generalised to situations where Harris' theorem fails in order to prove
a 'weak' form of it. The range of possible applications includes a number
of stochastic PDEs and stochastic delay equations.
|
|
| 2008-11-13 |
Thu |
Dan Crisan (Imperial College) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Sequential Monte Carlo methods - a theoretical perspective
|
| |
| |
Abstract:
The aim of the talk is to present a bird's-eye view of sequential Monte
carlo
methods (including the SIR algorithm and branching algorithms) with
emphasis
on classical convergence results. Additionally, some recent uniformly
convergent particle filters will be discussed.
The second part of the talk is based on joint work with K. Heine (see
http://www.ma.ic.ac.uk/ dcrisan/crihei2.pdf for details)
|
|
| 2008-11-06 |
Thu |
Mark Steel (University of Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Time-Dependent Stick-Breaking Processes
|
| |
| |
Abstract:
This paper considers the problem of defining a time-dependent nonparametric prior. A recursive construction allows the definition of priors whose marginals have a stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals have interesting interpretations that are further investigated. We develop a general conditional MCMC method for inference in a wide subclass of these models. We derive a Polya urn scheme type representation of the Dirichlet process construction. This allows us to develop a marginal MCMC method for this case. The result section shows the relative performance of the two MCMC schemes for the Dirichlet process case and looks at two data examples.
|
|
| 2008-10-23 |
Thu |
Lucy Morecroft & Nick Fieller (Sheffield) |
RSS Seminar Series |
| 16:30 |
Hicks Room K14 |
Faces and Statistics
|
| |
| |
Abstract:
The study described here was undertaken to develop a statistical method for measuring the quality of match of photographs of faces taken at a scene of crime to that of a suspect. The objective was to provide evidential information of use in a court of law. The method is based on landmark identification of facial features and routine techniques of shape analysis to model their joint distribution, thus allowing a statistical assessment of facial identification.
|
|
| 2008-10-16 |
Thu |
Leo Bastos (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Diagnostics for Gaussian Process Emulators
|
| |
| |
Abstract:
This work presents some diagnostics to validate and assess the adequacy of a
Gaussian process emulator as surrogate for a computer model. These diagnostics
are based on comparisons between simulator outputs and Gaussian process
emulator outputs for some test data, known as validation data, defined by a
sample of simulator runs not used to build the emulator. Our diagnostics take
care to account for correlation between the validation data. In order to
illustrate a validation procedure, these diagnostics are applied to two
different data sets.
|
|
| 2008-10-16 |
Thu |
Tom Fricker (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Prior specification in Gaussian process emulators: What do we mean by the mean?
|
| |
| |
Abstract:
When building an emulator for a computer model, we treat the model output as an
unknown deterministic function of the inputs. The data we have are observations
of the computer model output at a number of input points, and our task is to
make inference about the function using this noiseless data. We use a
semiparametric regression model, a priori describing the function as the sum of
a parametric mean function and a zero-mean Gaussian process.
Often in past a very basic regression function has been used for the mean
(either constant or linear in the inputs), and most of the effort has been
spent in correctly specifying the Gaussian process to model the residuals.
However, in some quarters it is believed that we should attempt to build more
prior information about the computer model into the emulator via the mean
function. But individual realisations of a zero-mean Gaussian process do not
necessarily have a mean value of zero, so what exactly is meant when we talk
about `the prior mean' of the model? How far should we go in the mean
function's complexity? What happens if we overfit it? And does this extra
effort actually improve the emulator's predictions of the computer model? In
this talk I shall use some very simple toy examples to explore these questions
(but without necessarily offering any answers...)
|
|
| 2008-10-09 |
Thu |
Richard Wilkinson (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Estimating Species Divergence Times Using the Fossil Record
|
| |
| |
Abstract:
In this talk I will show how to estimate species divergence times using the
fossil record. I will describe how branching process models can be conditioned
to contain subtrees originating at a given point in time, and how these can be
used to model evolution taking some known phylogenetic structure into account.
Inference can be performed using Approximate Bayesian Computation (ABC) and I
will describe a hybrid ABC-Gibbs algorithm that can improve the efficiency of
the basic ABC algorithm.
|
|
| 2008-10-07 |
Tue |
Tom Bridgeland (Sheffield) |
SoMaS Colloquium |
| 17:00 |
LT7 |
Mirror Symmetry |
| |
| |
Abstract:
Since its discovery by string theorists in the early 90s mirror
symmetry has become a huge area of research with connections to many
areas of mathematics. I'll try to give a rough feel for the subject by
introducing Calabi-Yau manifolds and explaining what it means for two such
manifolds to be mirror.
|
|
| 2008-06-05 |
Thu |
David Lucy (University of Lancaster) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
|
|
| 2008-05-22 |
Thu |
Neil O'Connell (University of Warwick) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Exponential functionals of Brownian motion and class one Whittaker functions
|
| |
| |
Abstract:
Motivated by a problem concerning scaling limits for directed polymers, and recent
extensions of Pitman's `2M-X' theorem including an analogue, due to Matsumoto and
Yor, for exponential functionals of Brownian motion, we consider (multi-dimensional)
Brownian motion conditioned on the asymptotic law of a family of exponential functionals
and identify which laws give rise to diffusion processes. For particular families (with a lot
of symmetry) these conditioned processes are related to class one Whittaker functions
associated with semisimple Lie groups. The work of Matsumoto and Yor corresponds to the
group GL(2,R) and the class one Whittaker function in this case is essentially the Macdonald
function (or modified Bessel function of the second kind). For the group GL(3,R) many
explicit formulae are available for understanding the behaviour of these processes.
The directed polymer problem should correspond to the group GL(n,R) and the asymptotics
of the corresponding Whittaker functions for large n, but there are significant technical
hurdles to overcome before this can be made fully rigourous. This is based on joint work
with Fabrice Baudoin.
|
|
| 2008-05-21 |
Wed |
Michael Atiyah (Edinburgh) |
SoMaS Launch Event |
| 09:00 |
Lecture theatre 7 |
Soliton dynamics
|
| |
| |
Abstract:
Many important physical problems involve non-linear PDE. Simplified models may admit exact analytical solutions, which can provide some guidance, but usually this has to be augmented by simulation, backed by physical insight. There is scope here for a really interdisciplinary approach.
I will illustrate this by the example of magnetic monopoles and the Skyrmion model of protons and neutrons, showing in particular the underlying role of topology.
|
|
| 2008-05-21 |
Wed |
Douglas Gough (Cambridge) |
SoMaS Launch Event |
| 10:00 |
Lecture theatre 7 |
Resonant waves in a deformed sphere
|
| |
| |
Abstract:
The resonance conditions for one-dimensional waves on a line are easy to derive and state. Brillouin, and perhaps Einstein, tried to generalize them to three dimensions in the early days of quantum theory. Unfortunately, their analyses were incomplete. It was only after Keller, nearly forty years later, recognized the importance of caustic surfaces that useful estimates of the eigenvalues of wave-like boundary-value problems were obtained, and then the resonance procedure became widely used to solve complicated problems. But I shall keep it simple. After describing the basic procedure, and applying it to acoustic waves in a spherical system, which could be a nonrotating star, I shall demonstrate how small deformations caused by rotation or a magnetic field can be accounted for, yielding asymptotic formulae which provide more insight than do more accurate numerical solutions.
|
|
| 2008-05-21 |
Wed |
Terry Lyons (Oxford) |
SoMaS Launch Event |
| 11:30 |
Lecture theatre 7 |
Rough paths
|
| |
| |
Abstract:
Calculus is the main mathematical tool used to describe systems
with a local interaction. Examples of this abound throughout
mathematics. Even the simplest case of a control problem without
feedback has a huge importance. Differential equations of the
form dyi = ∑i fi,j dxi express the relationship between
a controlling process x and a response y; x could be a path in a
Lie algebra and y its development into a Lie group; x could
represent the evolution of massive particles exerting a
gravitational influence on the evolution of a satellite, whose
state is represented by y.
However, an examination of many real world situations leads one to
conclude that in many contexts, the controls that influence
evolution are highly oscillatory and not at all adequately
modelled on normal scales by classical tools of calculus. The
theory of rough paths considers the relationship between the
control and the response, and identifies natural metrics making
this functional uniformly continuous, and so well-defined on the
completion. The completion of the smooth paths in these metrics
are called rough paths; they are tractable and not particularly
abstract objects (it is important to understand that they are a
generalisation of the concept of a smooth path, rather than a
restriction of the concept of a continuous path). They allow one
to describe what is important about x on normal scales and to do
numerical analysis on these scales, rather than tunnel deep into
fine structure to use classical calculus.
A key feature of this approach is a natural and universal
representation of the class of paths in Rn with
concatenation into a subgroup of the free tensor algebra.
|
|
| 2008-05-21 |
Wed |
Jon Keating (Bristol) |
SoMaS Launch Event |
| 14:00 |
Lecture theatre 7 |
Random matrices and number theory
|
| |
| |
Abstract:
I will review some conjectural connections between the zeros of the Riemann zeta function and random matrix theory, which underpins our understanding of complex quantum systems. I will then describe how these conjectures shed interesting new light on some deep and long-standing problems relating to the size of the Riemann zeta function and other L-functions, and the number of rational points on elliptic curves.
|
|
| 2008-05-21 |
Wed |
Paul Blackwell (Sheffield) |
SoMaS Launch Event |
| 15:00 |
Lecture theatre 7 |
Random tessellations - models, inference and applications
|
| |
| |
Abstract:
Tessellations with various kinds of symmetry and regularity are well known in mathematics and in art, but tessellations generated by random processes are also important, and have been widely used as models of observed spatial patterns. Statistical inference for such processes can enable us to choose between models or theories, to reconstruct patterns or images, or to estimate underlying parameters. I will talk about a range of tessellations of the plane, including the well-known (and often re-invented) Dirichlet or Voronoi tessellation and variants obtained by for example varying the distance function used, regarding the plane as a section of a three-dimensional space, or using a form of duality-giving the Delaunay triangulation. The random process driving the tessellation will typically be a point process on some suitable space; in practice, a further modelling step is needed to describe the way in which the tessellation is observed, for example the `noise' in an image. Carrying out the actual inference involves modern computer-intensive `Markov chain Monte Carlo' techniques, which are partly derived from simulation techniques in physics. I will illustrate the models and methods with examples from ecology and a selection of possible other areas including material science, physiology, geography and astronomy.
|
|
| 2008-05-21 |
Wed |
Koji Ohkitani (Sheffield) |
SoMaS Launch Event |
| 16:10 |
Lecture theatre 7 |
Recent progress in the basic problems of fluid equations
|
| |
| |
Abstract:
In this talk geared for non-specialists, we address the fundamental issues of fluid dynamics. Besides their mathematical interest as nonlinear PDEs, we explain the esoteric connection with developed fluid turbulence, centering on the so-called Onsager's conjecture.
We then review what have been known mathematically regarding the 3D incompressible Euler and Navier-Stokes equations and point out the differences from what physicists and engineers expect about them.
We recall how the existing methods fail to show, for example, regularity of the Navier-Stokes equations or singularity of the Euler equations. We also emphasise how studying the Euler equations may help in making possible progress in the Navier-Stokes theory. Some examples of numerical experiments are shown for illustration, where appropriate.
|
|
| 2008-05-21 |
Wed |
Neil Strickland (Sheffield) |
SoMaS Launch Event |
| 16:50 |
Lecture theatre 7 |
Thoughts on toric topology
|
| |
| |
Abstract:
In this talk I'll discuss a construction that starts with some combinatorial and algebraic data and produces a manifold, called a toric variety. There are many beautiful examples, and connections with combinatorics, commutative algebra, geometry, topology and physics, so this topic lies in the intersection of many of the most active areas of research in the pure mathematics department.
|
|
| 2008-05-15 |
Thu |
Jenny Freeman (University of Sheffield) |
RSS Seminar Series |
| 16:30 |
John Pemberton Room, 2nd Floor, ScHARR |
How to Display Data
|
| |
| |
Abstract:
The speaker will illustrate various good and poor methods of displaying data,
particularly in medical research, taken in part from her recent book. She will give tips
on how to improve the way data are displayed, both in publications and in talks.
|
|
| 2008-05-08 |
Thu |
Owen Jones (University of Melbourne) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Looking for continuous local martingales
|
| |
| |
Abstract:
Continuous local martingales, or equivalently time-changed Brownian
motion, are a popular class of models in finance. We present a set
of statistical tests for whether or not an observed process is a
continuous time-changed Brownian motion, based on the concept of the
crossing tree.
We apply our methodology to five currency exchange rates-AUD-USD,
JPY-USD, EUR-USD, GBP-USD and EUR-GBP-and show that in each case,
when viewed at a moderately large time scale, the log-transformed
series is consistent with a continuous local martingale model.
|
|
| 2008-04-28 |
Mon |
Simon Willerton (Sheffield) |
Quantisation |
| 16:10 |
J11 |
K-theory
|
|
| 2008-04-24 |
Thu |
Leszek Roszkowski (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Bayesian Statistics in Cosmology and Particle Physics
|
| |
| |
Abstract:
I will describe two recent applications of Bayesian
statistics. In one, main features of our Universe are extracted from
studies of cosmic background radiation. In the other, current data is
used to speculate about properties of "new physics" models based on
supersymmetry that will soon be tested in particle physics experiments
at the Large Hadron Collider (LHC) at CERN near Geneva.
|
|
| 2008-04-17 |
Thu |
Adam Butler (BioSS Edinburgh) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
A latent Gaussian model for compositional data with many zeros
|
| |
| |
Abstract:
Compositional data record the relative proportions of different components within a mixture, and arise frequently in many fields, including geology, ecology and human health. Standard statistical techniques for the analysis of such data assume the absence of proportions which are genuinely zero, but real data may contain a substantial number of zero values. In this talk I will present a latent Gaussian model for the analysis of compositional data which contain zero values, based on assuming that the data arise from a (deterministic) Euclidean projection of a multivariate Gaussian random variable onto
the unit simplex. A simulation study is used to compare three difference methods of inference - maximum likelihood estimation, MCMC and approximate Bayesian computation - and the methodology is illustrated using real data on dietary intake.
|
|
| 2008-04-10 |
Thu |
Oliver Johnson (University of Bristol) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Maximum entropy and Poisson approximation
|
| |
| |
Abstract:
I will show that the Poisson distribution maximises entropy in the class of
ultra log-concave distributions (a class which includes sums of Bernoulli
variables). I will also explain how this result relates to bounds in
Poisson and compound Poisson approximation.
|
|
| 2008-03-13 |
Thu |
Robert Gramacy (University of Cambridge) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Importance Tempering
|
| |
| |
Abstract:
Simulated tempering (ST) is an established Markov Chain Monte
Carlo (MCMC) methodology for sampling from a multimodal density π(θ).
The technique involves introducing an auxiliary variable k taking values in
a finite subset of [0,1] and indexing a set of tempered distributions, say
πk(θ) = π(θ)k. Small values of k encourage better mixing, but
samples from π are only obtained when the joint chain for (θ,k) reaches
k=1. However, the entire chain can be used to estimate expectations under pi
of functions of interest, provided that importance sampling (IS) weights are
calculated. Unfortunately this method, which we call importance tempering
(IT), has tended not work well in practice. This is partly because
the most immediately obvious implementation is naïve and can lead to high
variance estimators. We derive a new optimal method for combining multiple
IS estimators and prove that this optimal combination has a highly desirable
property related to the notion of effective sample size. The methodology is
applied in two modelling scenarios requiring reversible-jump MCMC, where the
naïve approach to IT fails: model averaging in treed models, and model
selection for mark-recapture data.
|
|
| 2008-03-13 |
Thu |
Russ Bentley, Carol Calvert, Will Driskell, Mike Jones, Nicky Tarry (Department for Work & Pensions) |
RSS Seminar Series |
| 16:15 |
Conference room 1 - Moorfoot Building |
Statisticians from DWP talk about their work
|
| |
| |
Abstract:
Statisticians from the Department for Work and Pensions' Information Directorate will provide an insight into the impact statisticians have in the UK's largest Government Department. They will show the contribution statisticians can make to producing accurate intelligence on fraud and migration, how their work has supported policy development and describe how their career as a professional statistician has had an impact and been rewarding.
|
|
| 2008-03-10 |
Mon |
Richard Hepworth (Sheffield) |
Quantisation |
| 16:10 |
J11 |
The Hirzebruch Signature Theorem
|
|
| 2008-02-28 |
Thu |
Michael Papathomas (Imperial College London) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Obtaining proposal distributions for reversible jump MCMC
|
| |
| |
Abstract:
A major difficulty when implementing the reversible jump Markov chain Monte Carlo methodology lies in the choice of good proposals for the parameters of the competing statistical models. We
focus on the comparison of non-nested log-linear models and present a novel approach for the construction of proposal distributions.
|
|
| 2008-02-26 |
Tue |
Michael Thompson (Sheffield) |
SoMaS Colloquium |
| 17:00 |
Hicks Lecture Theatre 7 |
Forward and Inverse Problems of Solar Seismology
|
| |
| |
Abstract:
The Sun oscillates simultaneously in more than a million resonant modes, the oscillations being manifest in small-amplitude motions of the Sun's surface. The measured properties of the observed oscillations can be used to infer conditions inside the Sun, a study known as helioseismology. In this colloquium I shall describe the forward problem of modelling the oscillations and the inverse problems that arise in using the oscillations to infer properties of the solar interior and its physics.
|
|
| 2008-02-18 |
Mon |
|
Quantisation |
| 16:00 |
J11 |
Organisational Meeting
|
|
| 2008-02-14 |
Thu |
Rita Zapata-Vasquez (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Bayesian cost-effectiveness analysis based on a decision analytic model
|
| |
| |
Abstract:
The purpose of economic evaluations relating to cost-effectiveness analysis is to provide decision-makers with sufficient evidence to establish the relevance or pertinence of one treatment or strategy over another, or to adjust the results to his/her location of interest.
Cost-effectiveness studies based on decision models involve highlighting specific features of previously published studies. However, the lack of evidence or of consistent reports is common in many fields. In medicine this is complicated by the fact that it is ethically unacceptable to implement clinical trials that put patients under a high risk, or because the cost of such trial is not affordable. Apart from the specialized literature, another source of information is that which can be obtained from experts through the use of elicitation. Regardless of the origin, from this knowledge judgements are established to represent the uncertainty of the data through the use of probability distributions.
A model for assessing the cost-effectiveness of two management strategies for the treatment of intracranial hypertension in children with severe traumatic brain injury is outlined. Some parts of the model structure will be presented, but I will focus on the way that the uncertainty of the parameters (inputs) of the model were formulated as probability distributions, based on the corresponding judgements.
Certain dependence relations among inputs will be shown, and how learning from one aspect may change our beliefs. Further, I will comment on how the dependence can be conceived when cost and effects come from different sources.
|
|
| 2008-02-14 |
Thu |
Theresa Cain (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Bayesian Inference for health state utilities using pairwise comparison
data
|
| |
| |
Abstract:
The National Institute for Health and Clinical Excellence (NICE) makes
recommendations about which drugs should be available on the NHS. An important
part of this decision is performing a cost-effectiveness analysis. When
evaluating the cost-effectiveness of a treatment, it is important to consider
the quality of life a patient experiences. The quality of life is described by
utility, a measure of preference for a particular health condition.
Conventional methods of eliciting utilities such as the Standard Gamble and
Time Trade-off involve questions that some respondents might find difficult to
answer. An alternative method is to collect discrete choice data, in which
respondents simply state which health state they prefer from two alternatives,
rather than provide actual utilities. The underlying utilities must be
determined given these pair-wise choices. We consider Bayesian approaches for
inference about population utilities given such pair-wise choice data.
|
|
| 2008-02-07 |
Thu |
John Haslett (Dublin Trinity College) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Monotone smoothing: application of a compound Poisson- Gamma process to
modelling radiocarbon-dated depth chronologies
|
| |
| |
Abstract:
We propose a new and simple continuous Markov monotone stochastic
process and use it for Bayesian monotone smoothing. The process is piece-wise
linear, based on additive independent Gamma increments arriving in a Poisson
fashion. A special case allows very simple conditional simulation of sample
paths given known values of the process. We take advantage of a
re-parameterisation involving the Tweedie distribution to provide efficient
MCMC computation. The motivating problem is the establishment of a chronology
for samples taken from lake sediment cores; that is, the attribution of a set
of dates to samples of the core given their depths, knowing that the age-depth
relationship is monotone. The chronological information arises from radiocarbon
(14C) dating at a subset of depths. We use the process to model the
stochastically varying sedimentation rate.
|
|
| 2007-12-10 |
Mon |
Dave Applebaum (Sheffield) |
Quantisation |
| 17:00 |
J11 |
The Heat Equation
|
|
| 2007-11-29 |
Thu |
Boris Mitavskiy (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Complexity of Evaluating the Probability Distribution of State Cycles in Finite State Update Networks
|
| |
| |
Abstract:
In many situations in biology (gene interactions,
metabolic pathways, etc) and communications (mobile phones, WWW) an
appropriate model is provided by a digraph in which the nodes
(genes, metabolites, phones, computers) are in various states, and
these states are updated (at times t=0, 1, 2, …) as a
response to the states of the "incoming nodes". Assuming
synchronous updating then the state of the system as a whole U(t)
say is some function of U(t−1). The dynamics of the system (i.e.
the sequence of U(t)) can then be described by a directed graph
over the possible states, where two states x and
y are joined if U(t−1)=x implies
U(t)=y. Since the system is finite this directed graph
consists of a set of cycles, and a set of trees each rooted (the
edges of each tree pointing towards the root) on the cycles.
There is much known (but little understood) about these dynamics. In
this talk I'll introduce a rigorous simplified model of this
scenario and study its basic properties with respect to the
distribution of cycle lengths. It turns out that the distribution of
fixed points is rather straightforward to compute (and it is the
uniform distribution regardless of the network topology!) while the
distribution of cycles of length k for any fixed k ≥ 2 is
already an NP-hard question with respect to the size of the
underlying digraph. I will provide a brief introduction to the
theory of NP-completeness which is sufficient to understand the
proofs. If time allows, I will also discuss a constant time
algorithm to solve the subproblem where the underlying digraph is an
r-input regular one.
|
|
| 2007-11-22 |
Thu |
Qiwei Yao (London School of Economics) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Modelling Multiple Time Series via Common Factors
|
| |
| |
Abstract:
We propose a new method for estimating common factors of multiple
time series. One distinctive feature of the new
approach is that it is applicable to nonstationary time
series. The unobservable (nonstationary) factors are
identified via expanding the orthoganal complement of the factor
loading space step by step; therefore solving a high-dimensional
optimization problem by many low-dimensional sub-problems. Asymptotic
properties of the estimation were investigated. The proposed methodology
was illustrated with both simulated and real data sets.
|
|
| 2007-11-15 |
Thu |
John Harthman (South Yorkshire Fire & Rescue Service) |
RSS Seminar Series |
| 16:30 |
Hicks Room K14 |
Registering Risk - The Community Risk Register
|
| |
| |
Abstract:
Under the Civil Contingencies Act 2004, local authorities and the emergency services are required to assemble and publish a "register" of local hazards and the risks they pose to their communities as a basis for informing emergency planning. This talk will examine the principles widely adopted across the UK in fulfilling this legal duty and illustrate some areas of concern, with particular reference to the supposedly 'unprecedented' floods in Sheffield and South Yorkshire of June 2007.
|
|
| 2007-11-14 |
Wed |
Alexander J McNeil (Heriot-Watt University) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
A New Perspective on Archimedean Copulas
|
| |
| |
Abstract:
The Archimedean copula family is used in a number of actuarial applications, ranging from the construction of multivariate loss distributions to frailty models for dependent lifetimes. We present some new results that contribute to a greater understanding of this family and point the way to improved simulation and estimation procedures. We derive necessary and sufficient conditions for an Archimedean generator function (a continuous, decreasing mapping of the positive half-line to the unit interval) to generate a copula in a given dimension d. We also show how the Archimedean family coincides with the class of survival copulas of L1-norm symmetric distributions. These results allow us to construct a rich variety of new Archimedean copulas in different dimensions and to solve in principle the problem of generating samples from any Archimedean copula. The practical consequences include new models for negatively dependent risks, simple formulas for rank correlation coefficients and diagnostic tests for Archimedean dependence.
|
|
| 2007-11-08 |
Thu |
Markus Riedle (University of Manchester) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Introduction to stochastic delay differential equations
|
| |
| |
Abstract:
In the last years stochastic functional differential equations or stochastic
differential equations with
delay have gained increasing attention in several scientific areas such as
economy, biology, physics and
medicine. The reason can be found in the observation that in a huge variety of
models the evolution of the
process describing the dynamics in the model under consideration not only
depends on the current state of the
process but also on its former states. This effect is due to various reasons
such as time to maturity,
incubation time, time to build, time to transport, hysteresis, delayed feedback
and past dependent
volatility.
In the beginning of the talk we present some of these applications of stochastic
functional differential equations. We introduce the basic ideas of ordinary
stochastic
differential equations not depending on the past and explain how these equations
can be
generalised to functional equations covering the examples presented before. The
fundamental theory of stochastic functional differential equations are
introduced and in
particular compared with the situation of ordinary stochastic differential
equations.
In the remaining part of the talk we distinguish several cases how the random
noise and
past dependence enter the equation and we focus here on asymptotic aspects of
the
solution. We present some phenomena only known from delay equations. We also
introduce
some results which explain the relation of functional and partial stochastic
differential
equations.
|
|
| 2007-10-22 |
Mon |
Paul Mitchener (Sheffield) |
Quantisation |
| 17:00 |
J11 |
Motivation and Introduction to the Index Theorem |
| |
| |
Abstract:
We will look at de Rham cohomology, the Euler characteristic, differential operators, and the Gauss-Bonnet formula in an attempt to motivate the Atiyah-Singer index theorem before stating the theorem in its general form.
The plan is for this to be a short talk; we will work out organisational details for the rest of the semester afterwards.
|
|
| 2007-10-18 |
Thu |
Steve Buckland (The National Centre for Statistical Ecology) |
RSS Seminar Series |
| 14:30 |
Hicks Room K14 |
Embedding population dynamics models in inference
|
| |
| |
Abstract:
Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the consequences of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the response of populations to anthropogenic change, while handling the major sources of uncertainty. We describe a simple ‘building block’ approach to formulating discrete-time models. These models may include demographic stochasticity, environmental variability through covariates or random effects, multi-species dynamics such as in predator-prey and competition models, movement such as in metapopulation models, non-linear effects such as density dependence, and mating models. We discuss methods for fitting such models to time series of data, and quantifying uncertainty in parameter estimates and population states, including model uncertainty, using computer-intensive Bayesian methods.
|
|
| 2007-10-18 |
Thu |
Rachel Borysiewicz (The National Centre for Statistical Ecology) |
RSS Seminar Series |
| 14:30 |
Hicks Room K14 |
Integrated population modelling for multi-site data
|
| |
| |
Abstract:
The statistical analysis of mark-recapture-recovery (MRR) data collected on wild animal populations dates back to the 1960s, when the foundation was laid for stochastic models fitted to data by the method of maximum likelihood. In recent years an active area of research has developed which combines MRR data with census data. The census data can be described by state-space models and the Kalman filter provides a mechanism for forming the census likelihood. Model fitting then follows by maximising a combined likelihood that is the product of component likelihoods. By combining multiple data sources it has been found that as well as increasing precision of common parameters, it is also possible to estimate parameters which would be inestimable from the analysis of the separate data alone. This methodology is termed integrated population modelling. A particular focus of this talk will be to discuss integrated population modelling for multi-site data, which arises when animals live in and move between different locations. By making use of movement information provided by MRR data, it is possible to avoid flat likelihood surfaces, thus allowing the estimation of site-dependent parameters. The benefits of performing integrated population modelling on multi-site data will be highlighted through both simulated and real data applications.
|
|
| 2007-10-18 |
Thu |
Toby Reynolds (The National Centre for Statistical Ecology) |
RSS Seminar Series |
| 14:30 |
Hicks Room K14 |
Integrated data analysis in the presence of emigration and tag loss:
A study of common guillemots on (and off) the Isle of May
|
| |
| |
Abstract:
In recent years, many UK seabird populations have experienced dramatic breeding failures and lower than average survival. The common guillemot (Uria aalge) is among those species to suffer. The causes of these events are likely due to a combination of over-fishing and environmental change affecting their primary prey species, the lesser sandeel (Ammodytes marinus). We need to understand the dynamics of seabird populations, in order to determine the implications of future breeding failures and enable us to monitor or predict the effects of future changes in the marine environment. Integrated population modelling provides a useful and robust means to achieve this.
An integrated analysis will be presented of four long-term datasets relating to a single guillemot colony on the Isle of May, southeast Scotland (a population of about 20,000 breeding pairs). These comprise abundance, MRR (two datasets) and productivity data. A particular complication with guillemot population dynamics arises due to unobservable emigration of immature birds. In traditional analyses using only MRR data, emigration is confounded with tag loss in the estimation of `fidelity' probabilities, and it is only possible to estimate their product. By combining all available data for the Isle of May guillemots, we are able to provide separate estimates for emigration and tag loss. This model provides a framework which may be used for prediction under various future scenarios.
|
|
| 2007-10-11 |
Thu |
Richard Jacques (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Classification Methods for the Analysis of High Content Screening Data
|
| |
| |
Abstract:
The current paradigm for the identification of candidate drugs within the pharmaceutical industry typically involves the use of high throughput screens. A high throughput screen allows a large number of compounds to be tested in a biological assay in order to identify any activity inhibiting or activating a biological process. From each of the assays run through a high throughput screen a high content screen image is produced which can be analysed using advanced imaging algorithms to produce a set of variables which reflect the observed activity of the cells within the image.
Classification methods have important applications in the analysis of high content screening data where they are used to predict which compounds have the potential to be developed into new drugs. Statistical approaches have been developed that enable classification using a single parameter. However, approaches for multi-parametric selection are still in their infancy. Furthermore, proper exploitation of the information contained within each high content screen image will enable more refined compound selection.
A new classification technique for the analysis of data from high content screening experiments will be presented and the methodology illustrated on an example data set using a random forest classifier.
|
|
| 2007-10-11 |
Thu |
Michailina Siakalli (University of Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
Hicks Room K14 |
Stochastic Stabilization
|
| |
| |
Abstract:
In simple words stability of a dynamic system means sensitivity of the system
to changes.
Consider a first order non-linear differential equation system
dx(t)f(x(t)).
Investigating what happens when noise is added, it has so far been observed
that Brownian motion noise can stabilize an unstable system or destabilize it in
the case that is stable. In my talk I will describe what is happening when the
given non-linear system is perturbed by different types of Poisson noise.
|
|
| 2007-10-09 |
Tue |
David Applebaum (Sheffield) |
SoMaS Colloquium |
| 17:00 |
Hicks Lecture Theatre 7 |
Some Random Thoughts on the Laplacian
|
| |
| |
Abstract:
The Laplacian is one of the most important linear operators in
mathematics. One reason for this is its ubiquitous role in important second
order partial differential equations (pdes) and this lecture will focus mainly
on the heat equation. I'll describe the probabilistic method of solving this
pde using Brownian motion and show how this relates to the modern
analytical approach via semigroup theory. In the last part of the talk, we'll
bring in some geometry and I'll describe how the Laplacian on a compact
Riemannian manifold can yield information about the curvature.
|
|
| 2007-05-31 |
Thu |
Mark Davis (Imperial) |
Probability and Statistics Seminar |
| 14:00 |
|
|
|
| 2007-05-10 |
Thu |
Simon Tavaré (Southern California) |
Probability and Statistics Seminar |
| 14:00 |
|
Stochastic processes in stem cell evolution |
|
| 2007-05-03 |
Thu |
Chris Williams (Edinburgh) |
Probability and Statistics Seminar |
| 14:00 |
|
Gaussian processes and machine learning |
|
| 2007-03-22 |
Thu |
Søren Asmussen (Aarhus) |
Probability and Statistics Seminar |
| 14:00 |
|
Tail Probabilities for a Computer Reliability Problem |
|
| 2007-02-22 |
Thu |
Ed Cripps (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
|
Variable selection and covariance selection in multivariate Gaussian linear regression |
|
| 2007-02-08 |
Thu |
Elke Thonnes (University of Warwick) |
Probability and Statistics Seminar |
| 14:00 |
|
Statistical analysis of pore patterns in fingerprints |
|
| 2006-12-14 |
Thu |
Stefanie Biedermann (Southampton) |
Probability and Statistics Seminar |
| 14:00 |
|
Robust optimal designs for dose-response experiments |
|
| 2006-12-07 |
Thu |
Raj Bhansali (Liverpool) |
Probability and Statistics Seminar |
| 14:00 |
|
Frequency Analysis of Chaotic Intermittency Maps with Slowly Decaying Correlations |
|
| 2006-11-30 |
Thu |
Goran Peskir (Manchester) |
Probability and Statistics Seminar |
| 14:00 |
|
Optimal stopping |
|
| 2006-11-23 |
Thu |
Stuart Barber (Leeds) |
Probability and Statistics Seminar |
| 14:00 |
|
Signal processing using complex Daubechies wavelets |
|
| 2006-11-16 |
Thu |
David Scott (Auckland) |
Probability and Statistics Seminar |
| 14:00 |
|
The hyperbolic and related distributions: problems of implementation |
|
| 2006-11-09 |
Thu |
Clive Anderson (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
|
Some Extreme Value Problems in Metal Fatigue |
|
| 2006-11-02 |
Thu |
Nancy Nicholls (Reading) |
Probability and Statistics Seminar |
| 14:00 |
|
Getting Started: Data Assimilation for Very Large Inverse Problems in Environmental Science |
|
| 2006-10-05 |
Thu |
John Fry (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
|
The Mathematics of Financial Crashes |
|
| 2006-10-05 |
Thu |
Keith Harris (Sheffield) |
Probability and Statistics Seminar |
| 14:00 |
|
Statistical Modelling and Inference for Radio-Tracking. |
|
