### Applied Bayesian Inference B (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.

The block lecture gives an introduction to Bayesian methods and their applications. In addition to the material covered by the block lecture, basic mathematical theory of Bayesian methods will be developed in Applied Bayesian Inference A, which can be visited additionally.

# 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.

# Venue

The lecture takes place at the Allianz-Gebäude in room 1C-01 as announced. The Problem Class is rescheduled to the Steinbuch Centre for Computing (SCC), campus south, computer lab I. For directions take a look at the campus map (the SCC is marked by a red circle).

Students are advised to bring their account and password for the SCC. For participants who are not in possession of an account a guest account will be provided.

# Lecture material

Please bring the lecture notes with you. Additionally you need the handouts

Brief Introduction to WinBUGS,

Running WinBUGS in Batch Mode,

Convergence Diagnostics with CODA ,

DAG's and Doodles and

Running WinBUGS from within R.

To run the examples from "Brief Introduction to WinBUGS" and "Running WinBUGS in Batch Mode" the files

betabin1.txt,

betabin2.txt,

betabin3.txt,

betabinscript.txt,

betabindata.txt and

betabininits.txt

are needed.

# Material for the problem class

Please bring the assignments and the handout Introduction to R with you. The following files are needed for solving the assignments and can be downloaded during the problem class:

studentdata.txt,

studentdata.csv,

BinomialConf.txt,

ozone.txt,

dugongs.txt,

meta.txt,

CD4116b.txt,

epil.txt,

svmodel.txt,

returns.txt,

returns_n.txt,

model_clayton.odc,

clayton_R.txt and

stack.txt.

# 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.