SAEM algorithm, beyond the simulation step

The expectation-maximization (EM) algorithm is a powerful computational technique for maximum likelihood estimation in incomplete data models. When the expectation step cannot be performed in closed form, a stochastic approximation of the EM algorithm (SAEM) can be used. The convergence of the SAEM toward critical points of the observed likelihood has been proved, and its numerical efficiency demonstrated. However, sampling from the posterior distribution may be intractable or have a high computational cost. Moreover, despite appealing features, the limit position of this algorithm can strongly depend on its starting one. In this talk, we propose a method to overcome these two limitations: sampling from an approximation of the distribution in the expectation phase of the SAEM. After recalling some SAEM algorithm properties, we will present recent developments aiming at extending its applicability. In particular, we will concentrate our presentation on improving the simulation step, focusing on the tempering-SAEM. Inspired by the simulated annealing algorithm, the tmp-SAEM proposes to temper the posterior distribution of the SAEM sampling step to favor its convergence towards global maxima.