Is multiple imputation related to MCMC?
Markov chain Monte Carlo (MCMC) is a collection of methods for simulating random draws from nonstandard distributions via Markov chains. MCMC is one of the primary methods for generating MI’s in nontrivial problems. In much of the existing literature on MCMC (e.g. Gilks, Richardson & Spiegelhalter, 1996, and their references) MCMC is used for parameter simulation, for creating a large number of (typically dependent) random draws of parameters from Bayesian posterior distributions under complicated parametric models. In MI-related applications, however, MCMC is used to create a small number of independent draws of the missing data from a predictive distribution, and these draws are then used for multiple-imputation inference. In many cases it is possible to conduct an analysis either by parameter simulation or by multiple imputation. Parameter simulation tends to work well when interest is confined to small number of well-defined parameters, whereas multiple imputation is more attractiv
