To provide students with knowledge of modern Bayesian Statistical inference, an understanding of the theory and application of computational methods in statistics and stochastic simulation methods including MCMC, and experience of implementing the Bayesian approach in practical situations.
1. Introduction to Bayesian inference (1.1 1. Priors, likelihoods and posteriors , 1.2 2. Conjugate and non-informative prior densities , 1.3 3. Multiparameter situations , 1.4 4. Inference for normal mean and variance jointly)
2. Introduction to Simulation Methods and Markov Chain Monte Carlo technoques. (2.1 1. Simulation continuous random variables by transformation , 2.2 2. Rejection sampling methods, 2.3 3. Markov chain Monte Carlo methods, 2.4 4. The Metropolis-Hastings algorithm in Bayesian statistics , 2.5 5. Monitoring Performance)
3. Data Augmentation Methods and Applications to Real Life Study (3.1 1. Data augmentation DA for censored lifetimes , 3.2 2. DA for grouped data , 3.3 3. Fitting mixture distributions with data augmentation , 3.4 4. Implementation of Animals Case Study)
4. Bayesian Model Assessment (4.1 1. Bayesian model comparison, Bayes factors, and evidence., 4.2 2. Posterior predictive checks and p-values.)
By the end of the course, students should be able to do the following:
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SCQF Level: 9
Credits: 15