Tutorial: Generating samples from strange probability distributions

Peter Green, Institute for Risk and Uncertainty, University of Liverpool, UK When conducting a probabilistic analysis, we often end up having to generate samples from a probability distribution. This, for example, is a crucial part of Monte Carlo simulations. For better-known probability distributions (Gaussian, uniform etc.), some simple tricks allow us to generate samples without too much difficulty. For the more ‘strange-looking’ distributions – which commonly arise in a Bayesian analysis – the problem becomes more difficult. This tutorial describes methods which can be used to generate samples from generic probability distributions. They often form an essential part of a Bayesian analysis. The tutorial is aimed at beginners, and will cover basic sampling algorithms before describing Markov chain Monte Carlo (MCMC) and importance sampling algorithms. Sample Matlab code will also be provided.

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