STATS 331 Introduction to Bayesian Statistics

Below description edited in year: 2013

Points: 15

Prereqs: 15 points from STATS 201, 207, 208 or BIOSCI 209.

Credit: Final exam 60%, mid-semester test 20% and assignment 20%.

Textbooks: Notes will be available in class

Website: STATS 331 website

Bayesian Statistics is all about understanding and modelling uncertainty. Since uncertainty can arise in any field of study, the scope for applications is immense. The paper starts with a brief history of statistics, and shows that the Bayesian paradigm was how statistics was originally applied and how it went out of favour, to be largely replaced by the frequentist (classical) paradigm. Recently, the Bayesian paradigm has become extremely popular, due in part to the development of MCMC (Markov Chain Monte Carlo) methods that allow the results to be computed quite easily even in complex scenarios.

The Bayesian approach will be introduced for discrete distributions using the “Bayes Box”. An unknown parameter is treated as a random variable with a probability distribution that describes our uncertainty. When data are obtained, the probability distribution gets updated to form the latest understanding of the parameter called the posterior. After many of the foundational concepts have been developed using the Bayes Box, the continuous version of Bayes’ theorem will be developed and applied using the software package JAGS. The course will enable a student to practically perform the kind of analyses encountered in STATS 201/7/8 from a Bayesian perspective and will be an eye opener which could be the spark to revitalise your statistical career.

Topics studied include: Probability and uncertainty, the Bayesian approach, parameter estimation, hypothesis testing, MCMC methods, heirarchical models, Bayesian versions of ANOVA, regression, and time series.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2018) is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.