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.
• Conduct likelihood inference for parametric statistical models, including estimating parameters, constructing large-sample confidence intervals and conducting hypothesis tests.
• 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.

• 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.

36 Lectures and 12 Tutorials

Summative

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

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.