When the conditional expectation of a complete-data likelihood in an EM algorithm is analytically intractable, Monte Carlo integration is often used to approximate the E-step. While the resulting Monte Carlo EM algorithm (MCEM) is flexible, assessing convergence of the algorithm is a more difficult task than the original EM algorithm, because of the uncertainty involved in the Monte Carlo approximation. In this note, we propose a convergence criterion using a likelihood-based distance. Because the likelihood is approximated by Monte Carlo integration, we make the distance small with a large probability by selecting the Monte Carlo sample size adaptively at each step of the MCEM algorithm. We implement the proposed convergence criterion along with the simulation size selection in a one-way random effects model. The result shows that our MCEM iterations match the exact EM iterations closely.

By:* Jens C. Eickhoff, Jun Zhu, Yasuo Amemiya*

Published in: Statistics and Probability Letters, volume 67, (no 2), pages 161-71 in 2004

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