1 Markov Chain Monte Carlo Methods 1.1 Introduction 1.1.1 Integration problems in Bayesian inference 1.1.2 Markov Chain Monte Carlo Integration 1.1.3 Markov Chain 1.2 The Metropolis-Hastings Algorithm 1.2.1 Metropolis-Hastings Sampler 1.2.2 The Metropolis Sampler 1.2.3 Random Walk Metropolis 1.2.4 The Independence Sampler 1.3 Single-component Metropolis Hastings Algorithms 1.4 Application: Logistic regression