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What you will learn

• Bayes’ Theorem. Differences between classical (frequentist) and Bayesian inference.
• Posterior inference: summarizing posterior distributions, credible intervals, posterior probabilities, posterior predictive distributions and data visualization.
• Gamma-poisson, beta-binomial and normal conjugate models for data analysis.
• Bayesian regression analysis and analysis of variance (ANOVA).
• Use of simulations for posterior inference. Simple applications of Markov chain-Monte Carlo (MCMC) methods and their implementation in R.
• Bayesian cluster analysis.
• Model diagnostics and comparison.
• Make sure to answer the actual research question rather than “apply methods to the data”
• Using latent (unobserved) variables and dealing with missing data.
• Multivariate analysis within the context of mixed effects linear regression models. Structure, assumptions, diagnostics and interpretation. Posterior inference and model selection.
• Why Monte Carlo integration works and how to implement your own MCMC Metropolis-Hastings algorithm in R.
• Bayesian model averaging in the context of change-point problem. Pinpointing the time of change and obtaining uncertainty estimates for it.