ABSTRACT
This chapter introduces some general sampling methods. It explains standard sampling techniques such as inverse transform sampling, rejection sampling and importance sampling as well as Markov chains and Markov Chain Monte Carlo in an intuitive way. Sampling-importance-resampling combines ideas from rejection sampling and importance sampling. Rejection sampling is not suitable for high-dimensional problems due to the curse of dimensionality. Markov chains are an important building block for a class of sampling algorithms which can be applied to many different distributions and also scale well with dimensionality. The Metropolis—Hastings algorithm is an example of a class of algorithms known as Markov Chain Monte Carlo. The chapter introduces a technique which concentrates on the regions of space considered important.
