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A New Strategy for Using Monte Carlo EM to Maximize Intractable Likelihoods

Brian Caffo, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health

Controlling the Monte Carlo sample size within each EM step is essential to obtain consistent estimates from the Monte Carlo EM algorithm (MCEM). Our approach to this issue is governed by the ascent property enjoyed by the deterministic EM algorithm. Namely, the value of the likelihood is guaranteed to increase at each successive parameter estimate. This is not guaranteed in the most common ways of implementing MCEM. Our algorithm checks this at each step and then automatically increases the sample size if our current parameter estimate has not increased the value of the likelihood over the previous step. This means that, in contrast with standard approaches to MCEM, our likelihood based approach attempts to detect and discard parameter estimates that jump away from the ML value.