STAT314-22S2 (C) Semester Two 2022

# Bayesian Inference

15 points

Details:
 Start Date: Monday, 18 July 2022 End Date: Sunday, 13 November 2022
Withdrawal Dates
Last Day to withdraw from this course:
• Without financial penalty (full fee refund): Sunday, 31 July 2022
• Without academic penalty (including no fee refund): Sunday, 2 October 2022

## Description

This course explores the Bayesian approach to statistics by considering the theory, methods for computing Bayesian solutions, and examples of applications.

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 basics 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 parameters

The 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.

## Learning Outcomes

• Goal of the Course
• To teach students to apply Bayesian inference methods to a range of common problems.

The courses will:
• introduce the foundations of Bayesian inference
• introduce the use of statistical software WinBUGS and R.
• introduce numerical algorithms required for practical Bayesian inference.
• demonstrate application of Bayesian inference to a wide range of common problems
• provide some comparison of Bayesian inference to the classical frequentist methods
• give you experience in writing scientific and technical reports

You will be able to:
• choose appropriate method for analysis of your dataset
• use WinBUGS or R to perform your analysis
• be able to interpret the analysis results in such a way that a non-user of statistics can understand
• write a scientific and technical report.

## Prerequisites

15 points from 200 level MATH or EMTH, STAT210-299 or DATA203

## Assessment

4 Assignments 40%
Written Examination (3hrs) 60%

## Textbooks / Resources

Gelman, Andrew et al; Bayesian data analysis ; Third edition; CRC Press, 2014.

## Indicative Fees

Domestic fee \$802.00

International fee \$4,563.00

* 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 .

## All STAT314 Occurrences

• STAT314-22S2 (C) Semester Two 2022