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Bayesian Inference
This course explores the parametric Bayesian approach to Statistics by considering the theory, methods for computing Bayesian solutions, and examples of applications. The key advantage of the Bayesian approach is that it naturally provides probabilistic measures of uncertainty along with the inference.Topics that may be covered include:• foundations of Bayesian Statistics: Treating parameters as random variables, prior information about parameters, Bayes’ theorem for combining information• prior distributions: Conjugate priors including conjugate mixtures, objective priors such as the flat prior, Jeffreys’ prior and Zellner’s prior• bayesian estimation: Deriving the posterior distribution using Bayes’ theorem, credible intervals such as the highest posterior density interval and equal-tail interval• bayesian testing of composite hypotheses using a posterior distribution• bayesian model selection: Bayesian testing as a special case of model selection, prior and posterior model probabilities, Bayes factors, difficulties with use of improper prior distributions for model selection, use of the deviance information criterion• posterior predictive distributions for inference about future observations.• tools for computing Bayesian solutions such as numerical integration, Monte Carlo integration and Markov chain Monte CarloStatistical computations will be performed using the R software but students do not need to know R beforehand.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.
Through this course, you will be able to do the following for common parametric models:elucidate the similarities and differences between Bayesian and frequentist statisticsfind a conjugate prior distribution or an objective prior distributionderive a posterior distribution for a given prior distribution and check that the posterior distribution is a proper distributionobtain point estimates and interval estimates from a posterior distribution.test composite hypotheses using a posterior distributionevaluate posterior model probabilities, Bayes factors and the deviance information criterion, and use them for hypothesis testing or model selectionderive a posterior predictive distribution and use it to infer about future observations
Subject to approval of the Head of School.
Elena Moltchanova
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. After enrolling in the course, you will be able to access materials from the course web page in Learn at: http://www.learn.canterbury.ac.nz/ Students who have not used the R software before can refer to the following e-book available from the UC Library:A Beginner’s Guide to R, by Zuur, Ieno and Meesters (Springer, 2009).
STAT461 Homepage STAT314 Homepage Mathematics and Statistics Honours Booklet General information for students LEARN
Domestic fee $913.00
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 .