A Markov chain Monte Carlo method family in incomplete data analysis

A Markov chain Monte Carlo method family is a collection of techniques for pseudorandom draws out of probability distribution function. In recent years, these techniques have been the subject of intensive interest of many statisticians. Roughly speaking, the essence of a Markov chain Monte Carlo method family is generating one or more values of a random variable Z, which is usually multidimensional. Let P(Z) = f(Z) denote a density function of a random variable Z, which we will refer to as a target distribution. Instead of sampling directly from the distribution f, we will generate [Z(1), Z(2)..., Z(t),... ], in which each value is, in a way, dependant upon the previous value and where the stationary distribution will be a target distribution. For a sufficient value of t, Z(t) will be approximately random sampling of the distribution f. A Markov chain Monte Carlo method family is useful when direct sampling is difficult, but when sampling of each value is not.