### Applied Bayesian Inference A (Winter Semester 2010/11)

The lecture will be given by Prof. Dr. Renate Meyer, University of Auckland, Department of Statistics, an international expert in Bayesian methods and their applications.

# Schedule

This course consists of a block lecture

04.10.2010-08.10.2010: | Building 05.20, Room 1C-01 |

Mo.-Fr. 08.00-12.00 | |

Mo.-Fr. 14.00-16.00 (Exercise) |

in addition to a lecture, which takes place 3 times per week during the first half of the winter semester

20.10.2010-17.12.2010: | Building 05.20, Room 1C-04 |

We. 09.45-11.15 | |

Th. 09.45-11.15 | |

Fr. 11.30-13.00 (Exercise). |

The block lecture gives an introduction to Bayesian methods and their applications. It can be visited separately (see Applied Bayesian Inference B). In addition to the material covered by the block lecture, basic mathematical theory of Bayesian methods will be developed in the second part of this course.

# Overview

The lecture gives an introduction to Bayesian inference starting from first principles. The Bayesian approach is based on a different paradigm than the classical frequentist approach to statistical inference.

Over the last decade, the Bayesian approach has revolutionised many areas of applied statistics such as biometrics, econometrics, market research, statistical ecology and physics.

Although the Bayesian approach dates back to the 18th century, its rise and enormous popularity today is due to the advances made in Bayesian computation through computer-intensive simulation methods. Knowledge of Bayesian procedures and software packages will become indispensable in most areas where statistics is applied. Students will be using the software package R for Bayesian computation and will be introduced to WinBUGS.

Topics covered include: the Bayesian approach, conjugate distributions, prior specification, posterior computation, simulation methods including Markov chain Monte Carlo using the WinBUGS software, model checking, and applications to data analysis.

# Prerequisites

Basic knowledge in mathematics, especially analysis (differentiation/integration of functions of several variables), as for instance acquired in a 2-3 semester long introductory mathematics lecture, including introductory maths lectures for engineers, biologists, economists etc. We explicitly welcome students and researchers from other disciplines.

Basic knowledge of probability and statistics (probability density and distribution functions, moments, marginal and conditional distributions etc.), equivalent to at least one introductory lecture.

Knowledge of a programming language will be of advantage, especially familiarity with SPLUS, R or SAS/IML, as R will be used in the lecture.

# Additional material

This is a popular scientific paper from David Malakoff about Bayesian inference.

This is an overview about probability distributions which will be given as a handout in the lecture.

# References

Albert, J. (2007), Bayesian Computation with R, Springer, New York.

Aitkin, M. (2010) Statistical Inference :an Integrated Bayesian/Likelihood Approach, Chapman & Hall.

Gelman, A., J.B. Carlin, H.S. Stern, D.B. Rubin (2004), Bayesian Data Analysis, Chapman&Hall, London.

Gilks, W., Richardson, S., Spiegelhalter, D. (1996), Markov Chain Monte Carlo in Practice, Chapman&Hall, UK.

Lee, P.M. (2004), Bayesian Statistics: An Introduction, Halsted Press, New York.

Ntzoufras, I. (2009), Bayesian Modeling Using WinBUGS, Wiley, NY.

For a full list refer to the bibliography of the lecture.