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
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Derive the asymptotic behaviour of likelihood inference, including the asymptotic distribution of the maximum likelihood estimator and the log-likelihood ratio test statistic.
- Construct appropriate parametric statistical models for frequently encountered types of data.
- 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.
- Conduct likelihood inference for parametric statistical models, including estimating parameters, constructing large-sample confidence intervals and conducting hypothesis tests.
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
Type | Hours |
---|---|
Independent Study | 114 |
Teaching | 36 |
Total study time | 150 |
Resources & Reading list
Textbooks
Gelman, A, Carlin JB, Stern HS, Dunson DB, Vehtari, A and Rubin, DB (2014). Bayesian Data Analysis. CRC Press.
Wood, S (2015). Core Statistics. Cambridge University Press.
Box, GEP and Tiao, GC (1992). Bayesian Inference in Statistical Analysis. Wiley.
Wasserman, L (2003). All of Statistics: A Concise Course in Statistical Inference .. Springer..
Sujit K. Sahu (2022). Bayesian modeling of spatio-temporal data. Boca Raton: CRC Press.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
Method | Percentage contribution |
---|---|
Exam | 50% |
Coursework | 50% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
Method | Percentage contribution |
---|---|
Exam | 100% |