MAS274 Statistical Reasoning

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

Semester 2, 2014/15 10 Credits
Lecturer: Dr Miguel Juarez uses MOLE Reading List
Aims Outcomes Teaching Methods Assessment

Statistics is about learning from data - often uncertain and variable - about underlying regularities of the real world. At first sight the methods for statistical analysis can appear particular to each application. This unit however shows that they can be founded on simple universal principles of statistical reasoning. There are two principal forms of statistical reasoning, known as frequentist and Bayesian inference These principles simplify understanding and give powerful tools for analysing new problems. They form the basis for more specialist modules in Level 3/Level 4. The course will show how practical analyses follow from the principles, and will illustrate their power through a set of case studies of real-world problems from areas such as medicine, economics, technology and the environment.

Prerequisites: MAS202 (Advanced Calculus); MAS205 (Statistics Core)

The following modules have this module as a prerequisite:

MAS364Bayesian Statistics
MAS371Applied Probability
MAS464Bayesian Statistics
MAS465Multivariate Data Analysis


Outline syllabus

  • Inference and reasoning: the nature of statistical reasoning, inference and the likelihood function.
  • Case studies drawn from areas such as medicine, business, science, technology and the environment: will be introduced early in the module and used throughout to illustrate the applicability and power of the methods.
  • Likelihood: definition, examples, numerical calculation; maximum likelihood estimates and likelihood intervals.
  • Frequentist methods: inference rules, point estimation, interval estimation and hypothesis testing; unbiasedness, mean square error and minimum variance unbiased estimators; confidence intervals; null and alternative hypotheses, power and significance tests.
  • Bayesian methods: parameters as values of random variables, combination of prior information and observed data to yield a posterior distribution for a parameter, nature of prior information, use of posterior distribution to make summary statements an formal inferences about parameters.

Office hours

Tuesday 14h00-16h00



Aims

  • To formulate the process of inference in terms of parametric models.
  • To introduce both frequentist and Bayesian inferential frameworks.
  • To illustrate the scope of the principles with practical applications.

Learning outcomes

  • Understand the aims of statistical inference and the importance of likelihood as a tool that underlies the principal theories of inference.
  • Find maximum likelihood estimates and likelihood intervals and regions for simple models.
  • Understand the principles of frequentist inference.
  • Apply those principles to construct point estimates, confidence intervals and significance tests.
  • Combine prior information and observed data into a posterior distribution for a parameter.
  • Use the posterior distribution to make summary statements and formal inference about parameters.
  • Appreciate the differences between the likelihood, Bayesian and frequentist theories of inference.

Teaching methods

Lectures, tutorials, problem solving


22 lectures, 6 tutorials

Assessment

One formal 2 hour restricted open book examination.

Reading list

Type Author(s) Title Library Blackwells Amazon
B J.G. Kalbfleisch Probability and Statistical Inference Vol 2: Statistical Inference 519.2 (K) Blackwells Amazon
B P.M. Lee Bayesian Statistics: An Introduction 519.542 (L) Blackwells Amazon
C A. Azzalini Statistical Inference: Based on the Likelihood 519.54 (A) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop on Mappin Street.