17 Monte Carlo Methods

17.1 Sampling and Monte Carlo Methods

17.1.1 Why Sampling?

17.1.2 Basics of Monte Carlo Sampling

17.2 Importance Sampling

17.3 Markov Chain Monte Carlo Methods

17.4 Gibbs Sampling

17.5 The Challenge of Mixing between Separated Modes

17.5.1 Tempering to Mix between Modes

17.5.2 Depth May Help Mixing