Bayesian Statistics Using R

Bayesian approach is becoming increasingly popular in all fields of data analysis, including but not limited to epidemiology, ecology, economics, and political sciences. It also plays an increasingly important role in data mining and deep learning.

This program provides a practical introduction to applied Bayesian data analysis, combining theory, philosophy and computational facility with the emphasis on formulating and answering real life questions. The two courses provide a broad overview of the fundamentals of Bayesian inference via clear practical examples and may serve as a stepping stone towards any other, more specialized, topic in Bayesian statistics.

What you'll 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.