Implementing and Diagnosing the Stochastic Approximation EM Algorithm
Wolfgang Jank · Journal of Computational and Graphical Statistics · 2006
The stochastic approximation EM (SAEM) algorithm is a simulation-based alternative to the expectation/maximization (EM) algorithm for situations when the E-step is hard or impossible. One of the appeals of SAEM is that, unlike other Monte Carlo versions of EM, it converges with a fixed (and typically small) simulation size. Another appeal is that, in practice, the only decision that has to be made is the choice of the step size which is a one-time decision and which is usually done before starting the method. The downside of SAEM is that there exist no data-driven and/or model-driven recommendations as to the magnitude of this step size. We argue in this article that a challenging model/data combination coupled with an unlucky step size can lead to very poor algorithmic performance and, in particular, to a premature stop of the method. This article proposes a new heuristic for SAEM's step size selection based on the underlying EM rate of convergence. We also use the much-appreciated EM likelihood-ascent property to derive a new and flexible way of monitoring the progress of the SAEM algorithm. The method is applied to a challenging geostatistical model of online retailing.