Bayesian Learning

Aim

After completion of the course the student should at an advanced level be able to:

• account for the main differences between Bayesian and frequentist inference
• analyze basic statistical models using a Bayesian approach and correctly interpret the results
• critically analyze and use Bayesian models for prediction and decision making
• implement more advanced statistical models, including those occurring in current research problems, using modern simulation methods
• perform Bayesian model inference on practical problems using programming language applicable for statistical analysis

Content

The course covers the following topics:

• Subjective probability
• Bayes theorem
• Likelihood
• Prior and posterior distribution
• Regularization priors
• Classification
• Marginalization
• Posterior approximation
• Bayesian analysis of the following models: Bernoulli, Normal, Poisson, Multinomial, Multivariate normal; Linear and nonlinear regression, Binary regression
• Prediction
• Decision theory
• Markov Chain Monte Carlo, including Gibbs sampling
• Mixture models
• Bayesian variable selection
• Model selection