ABSTRACT
In this chapter, the authors discuss the stochastic methods provide a way to characterize entire probability distributions. Stochastic methods rely on random number generation. The authors refers to generating independent random realizations from a known distribution as Monte Carlo (MC) sampling. Two other stochastic sampling approaches are frequently mentioned in the Bayesian context: rejection sampling and slice sampling. Stochastic methods for approximating integrals are a massive area of research and they have been extended in a number of directions to handle more complicated integrals. Slice sampling, by contrast, relies on a sample of auxiliary variables to obtain a sample from the target distribution of interest. MC integration is a powerful tool that the authors can use to calculate moments of functions of random variables.
