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Bayesian Modelling A (MATH 34910)

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Administrative Information

  1. Unit number and title: MATH 34910 Bayesian Modelling A
  2. Level: H/6
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: in this form 2001/2002
  6. Unit Organiser: Vladislav Tadic
  7. Lecturer: Marcelo Pereyra
  8. Teaching block: 1
  9. Prerequisites: MATH20800 Statistics 2

Unit aims

This unit will introduce you to an alternative approach to statistical modelling and inference, with a rather different flavour from those taught elsewhere in our programmes. The main aims of the unit are to acquaint you with the basic concepts of Bayesian statistics, and to provide you with the necessary background and experience to apply Bayesian modelling techniques to realistic statistical problems.

General Description of the Unit

Bayesian statistics is an area that has grown rapidly in popularity over the past 15 years or so largely as a result of computational advances which have made the approach far more applicable. In this unit we will discuss the Bayesian approach to statistical analysis and modelling. We introduce the basic elements of Bayesian theory, beginning with Bayes theorem, and go on to discuss the applications of this approach to statistical modelling. Topics discussed will include the construction of prior and posterior distributions and hierarchical models, large sample inference and connections to non-Bayesian methods, model checking, and a brief introduction to the computational tools which make analysis possible (in particular Markov chain Monte Carlo methods).

Teaching Methods

Lectures, supported by problem sheets.

Learning Objectives

The students will be able to:

  • Understand and explain the theoretical basis for and range of applications of the Bayesian approach to statistical modelling;
  • Describe and construct realistic and appropriate statistical models to describe a wide variety of modelling situations;
  • Use and understand appropriate computational methodology within a Bayesian framework.

Assessment Methods

The assessment mark for Bayesian Modelling A is calculated from a 1½-hour written examination in April consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) are allowed, i.e., only calculators carring 'Faculty of Science approved sticker' will be allowed in the examination room.

Award of Credit Points

Credit points are gained by passing the unit.

Transferable Skills

In addition to the general skills associated with other mathematical units, you will also have the opportunity to gain practice in the following: computer literacy and general IT skills, use of Matlab as a programmable statistical package, interpretation of computational results, time-management, independent thought and learning, and written communication.

Texts

The following texts may be useful for reference:

  1. Gelman, A., Carlin, J.B., Stern, H.S. and Rubin, D.B. Bayesian Data Analysis, Chapman and Hall.
  2. J.-M. Marin and C. P. Robert. Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer-Verlag.  
  3. Robert, C.P. The Bayesian Choice, Springer-Verlag.
  4. J. M. Bernardo and A. Smith. Bayesian Theory, Wiley.
  5. Robert, C.P. and Casella, G., Monte Carlo Statistical Methods, Springer-Verlag.
  6. D. Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman and Hall.

Syllabus

Bayesian Statistics: Bayes theorem; prior and posterior distributions; prior specification and conjugacy; large sample properties; Bayes estimates and credible intervals.

Statistical Modelling: Hierarchical models, model checking.

Monte Carlo Methods: Gibbs sampling for hierarchical Bayes models.