Bayesian Statistical Learning

Bayesian inference treats all unknowns as random variables, and the core task is to update the probability distribution for each unknown as new data is observed. After introducing Bayes’ Theorem to transform prior probabilities into posterior probabilities, the first part of this subject introduces theory and methodological aspects underlying Bayesian statistical learning including credible regions, prior choice, comparisons of means and proportions, multi-model inference and model selection. The second part of the subject will cover practical implementations of Bayesian methods through Markov Chain Monte Carlo computing and real data applications, focusing on (generalised) linear models and concluding by exploring machine learning techniques such as Gaussian processes.