Likelihood and Bayesian Inference

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• 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.
• Construct appropriate parametric statistical models for frequently encountered types of data.
• Derive the asymptotic behaviour of likelihood inference, including the asymptotic distribution of the maximum likelihood estimator and the log-likelihood ratio test statistic.
• Conduct likelihood inference for parametric statistical models, including estimating parameters, constructing large-sample confidence intervals and conducting hypothesis tests.

• 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.

Teaching and learning methods

36 Lectures and 12 Tutorials

Resources & Reading list

Textbooks

Wood, S (2015). Core Statistics. Cambridge University Press.

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

Sujit K. Sahu (2022). Bayesian modeling of spatio-temporal data. Boca Raton: CRC Press.

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

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

Summative

This is how we’ll formally assess what you have learned in this module.