Bayesian Inference

Description

STAT314 and STAT461 introduce the Bayesian approach to Statistics using parametric models and inference problems that students are familiar with at this level. Usually, these are the Bernoulli, Poisson, normal and linear regression models used in problems such as parameter estimation, hypothesis testing, model selection and prediction. Comparisons with results from the frequentist approach, which students are more familiar with, will be made to highlight similarities and differences between the two approaches.

Topics that are usually 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 and Monte Carlo integration

Statistical 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.