The University of Southampton
Courses

# MATH6171 Likelihood and Bayesian Inference

## Module Overview

This module develops methods for conducting inference about parametric statistical models. The techniques studied are general and applicable to a wide range of statistical models, including simple models for identically distributed responses and regression models, as well as many more complex models which may be encountered in other modules.

### Aims and Objectives

#### Module Aims

The aims of the module are: to study general-purpose methods for conducting inference for parametric statistical models, justify these approaches theoretically, and apply these techniques in practice.

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Construct appropriate parametric statistical models for frequently encountered types of data.
• Conduct likelihood inference for parametric statistical models, including estimating parameters, constructing large-sample confidence intervals and conducting hypothesis tests.
• Derive the asymptotic behaviour of likelihood inference, including the asymptotic distribution of the maximum likelihood estimator and the log-likelihood ratio test statistic.
• Conduct Bayesian inference for parametric statistical models, including choosing a prior distribution, computing the posterior distribution in cases with conjugate and non-conjugate priors, and making predictions and decisions based on the posterior distribution.

### Syllabus

- Examples of statistical models, including simple models for identically distributed responses and regression models. - Likelihood: maximum likelihood estimation, score, information, Cramer-Rao lower bound and the asymptotic distribution of the maximum likelihood estimator. - Large-sample confidence intervals. - Hypothesis testing: Generalised likelihood ratio tests and asymptotic distribution of the log-likelihood ratio test statistic. - Concepts of Bayesian inference: prior distributions, posterior distributions and using the posterior distribution to make predictions and decisions. - Bayesian inference with conjugate prior distributions. - Markov Chain Monte Carlo methods for approximate sampling from the posterior distribution.

### Learning and Teaching

#### Teaching and learning methods

36 Lectures and 12 Tutorials

TypeHours
Teaching48
Independent Study152
Total study time200

Box, GEP and Tiao, GC (1992). Bayesian Inference in Statistical Analysis.

Casella, G and Berger, FL (2002). Statistical Inference.

Gelman, A, Carlin JB, Stern HS, Dunson DB, Vehtari, A and Rubin, DB (2014). Bayesian Data Analysis.

Wood, S (2015). Core Statistics..

Pawitan, Y (2013). In All Likelihood: Statistical Modelling and Inference using Likelihood.

Wasserman, L (2003). All of Statistics: A Concise Course in Statistical Inference.

### Assessment

#### Assessment Strategy

The assessment for the repeat candidates will be based completely on the final examination.

#### Summative

MethodPercentage contribution
Coursework 30%
Exam 70%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.