## MAS61003 Sampling Theory and Design of Experiments

 Semester 2, 2021/22 15 Credits Lecturer: Dr Kevin Walters Timetable Reading List Aims Outcomes Teaching Methods Assessment Full Syllabus

This module deals with two different areas where the important features are the planning before the data are collected, and the methods for maximising the information which will be obtained. The results of sample surveys through opinion polls, etc., are common in the media. The Sampling Theory component of the course introduces several different methods for obtaining samples from finite populations and considers which method is most appropriate for a given sampling problem. Experiments which aim to discover improved conditions are common in industry, agriculture, etc. The purpose of experimental design is to maximise the information on what is of interest with the minimum use of resources. The Experimental Design component of the course introduces some of the more important design concepts. The module also introduces the concept of a 'computer experiment' (as opposed to a physical experiment), and considers the problem of uncertainty in predictions from computer models.

Prerequisites: MAS223 (Statistical Inference and Modelling)
Not with: MAS370 (Sampling Theory and Design of Experiments)
No other modules have this module as a prerequisite.

## Outline syllabus

• Methods for selecting samples in sample surveys.
• Statistical inference for finite populations.
• Experimental design for linear models. Optimal designs and factorial experiments.
• Uncertainty and sensitivity analysis for computer model predictions.

## Aims

• introduce statistical ideas used in sample surveys;
• introduce statistical methods for the design of physical experiments, in particular where the analysis can be performed using linear modelling techniques
• introduce statistical methods for the design and analysis of computer experiments.
• enhance studentsâ€™ broader understanding of statistical methodology and develop their professional skills as applied statisticians.

## Learning outcomes

• describe some of the methods that can be used for drawing a sample from a population, for the purposes of estimating characteristics of the population, and discuss their advantages and disadvantages;
• assist in the design of a physical experiment, specifically by proposing the settings of the factors/covariates that should be selected for each experimental observation;
• identify opportunities for reducing bias and/or variation in a planned experiment or survey by applying the principles of good experimental design;
• use appropriate statistical methods for designing and analysing computer experiments, in particular, to investigate uncertainty in computer model predictions, implemented using R;
• communicate key issues/results within the methodology to non-experts.

## Teaching methods

There will be formal lectures, which will involve explanation of theoretical concepts and their application to worked examples. The motivation, rationale, advantages and disadvantages of the various methods taught will be discussed as appropriate, with examples given of communicating issues to a lay audience. Detailed lecture notes will be provided, which students will be expected to study in their own time to assimilate the material. Students will also be required to study some material independently, with support provided via Blackboard discussion boards.

20 lectures, no tutorials

## Assessment

One formal 2 hour written examination. All questions compulsory.

## Full syllabus

1. Experimental Design

• A review of linear models: matrix notation; least squares estimation; orthogonality; prediction; confidence regions.
• Optimality criteria: D-optimal, G-optimal, V-optimal and A-optimal designs.
• Completely randomised designs and randomised block designs.
• Latin squares and balanced incomplete block designs.
• Factorial designs: complete factorial designs; fractional factorial designs; screening experiments.
• Designs for mixture experiments.
• Continuous and exact designs, and the Generalised Equivalence Theorem.
2. Sampling Theory
• Simple random sampling.
• Stratified sampling.
• Cluster sampling.
• Ratio and regression estimators.
• Capture-recapture sampling
• Questionnaire design.
3. Computer experiments
• Uncertainty in computer model predictions.
• Probabilistic sensitivity analysis.

## Reading list

Type Author(s) Title Library Blackwells Amazon
B Barnett Sample Survey; Principles and Methods 519.6 (B) Blackwells Amazon
B Box, Hunter and Hunter Statistics for experimenters: design, innovation, and discovery 519.5(B) Blackwells Amazon
B Morris Design of experiments: an introduction based on linear models 001.434 (M) Blackwells Amazon
C Atkinson and Donev Optimum Experimental Designs 519.52 (A) Blackwells Amazon
C Box and Draper Empirical model building and response surfaces 519.52 (B) Blackwells Amazon
C Cornell Experiments with mixtures 519.52 (C) Blackwells Amazon
C Cox and Reid The theory of the design of experiments 519.52 (C) Blackwells Amazon
C Goos and Jones Optimal design of experiments : a case study approach 670.285 (G) Blackwells Amazon

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

Most books on reading lists should also be available from the Blackwells shop at Jessop West.