Implementation in Missing Data Models
Missing data models (introduced in §5.3.1) are a natural application for simulation, since they use it to replace the missing data part so that one can proceed with a “classical” inference on the complete model. However, this idea was slow in being formalized; that is, in going beyond ad hoc solutions with no theoretical justification. It is only with the EM algorithm that Dempster et al. (1977) (see §5.3.3) described a rigorous and general formulation of statistical inference through completion of missing data (by expectation rather than simulation, though). The original algorithm could require a difficult analytic computation for the expectation (E) step and therefore cannot be used in all settings. As mentioned in §5.3.4 and §5.5.1, stochastic versions of EM (Broniatowski et al. 1983, Celeux and Diebolt 1985, 1993, Wei and Tanner 1990b, Qian and Titterington 1991, Lavielle and Moulines 1997) have come closer to simulation goals by replacing the E-step with a simulated completion of missing data (but without preserving the entire range of EM convergence properties).
KeywordsHide Markov Model Posterior Distribution Prior Distribution Gibbs Sampler Stochastic Volatility
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