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Bayesian Inference
STAT314 and STAT461 introduce theory and application of Bayesian Inference. Due to recent advances in computing and to the existence of some relatively user-friendly software Bayesian methods are becoming more and more popular in many applied fields of study, including epidemiology, bioinformatics, ecology and archaeology. This course will cover the basic of Bayesian theory as well as introduce computing methods necessary for implementation of this theory in practice. In addition to generalised linear regression models, analysis of variance and basic tests, for which the results of Bayesian inference will be compared with those for the classical frequentist results, the course will demonstrate the attractive flexibility and multifacetedness of Bayesian methods considering such problems as threshold analysis, and Poisson change-point problems among others.Topics that are usually covered include:• Bayes’ Inverse Probability Formula and Bayes’ Theorem. The concepts of prior and posterior distributions. Posterior predictive distribution. Various types of prior distributions.• Bayesian model comparison and Bayesian model averaging.• Numerical tools for Bayesian estimation: Markov Chain Monte Carlo (MCMC) methods, Gibbs sampler and Metropolis-Hasting sampler.• Bayesian inference on linear regression models, generalised linear models, and mixed-effects models.• Treatment of missing data and latent parametersThe statistical computations will be performed using a combination of WinBUGS (a software for Bayesian inference) and R (a statistical software package). Prior knowledge of WinBUGS is not required. Prior knowledge of R is desirable.STAT461 students attend the same lectures and computer labs as STAT314 but will be assigned additional readings and assessment.Students who have done or are doing STAT314 cannot do STAT461.
The courses will:introduce the foundations of Bayesian inferenceintroduce the use of stastical software WinBUGS and R.introduce numerical algorithms required for practical Bayesian inference.demonstrate application of Bayesian inference to a wide range of common problemsprovide some comparison of Bayesian inference to the classical frequentist methodsgive you experience in writing scientific and technical reportsYou will be able to:choose appropriate method for analysis of your datasetuse WinBUGS or R to perform your analysisbe able to interpret the analysis results in such a way that a non-user of statistics can understandwrite a scientific and technical report.
Subject to approval of the Head of School.
Elena Moltchanova
Dr Patrick Graham
There will be two lectures and one computer lab per week for this course. Attendance at lectures and computer labs is mandatory because supervised instruction is essential for understanding the course material.The continual assessment consists of a series of exercises that must be submitted at specified times throughout the course. These exercises and their timings are designed to help you keep up with the course material. They also allow the lecturer to monitor progress and to provide assistance in a timely manner when needed.There will be three tests, one every four weeks, but no final exam.
Course materials will be provided and no textbook is needed.For those interested to learn more about Bayesian statistics, the recommended reading is:Gelman et al. Bayesian Data Analysis. 2nd ed. Chapman & Hall/CRC, 2004 (or later editions).
Mathematics and Statistics Honours Booklet General information for students LEARN
Domestic fee $932.00
International Postgraduate fees
* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.
For further information see Mathematics and Statistics .