Convergence of a stochastic approximation version of the EM algorithm

The expectation-maximization (EM) algorithm isa powerful computational tech nique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data m odels. In certain situations, however, this method is not applicable becaus e the expectation step cannot be performed in closed form. To deal with the se problems, a novel method is introduced, the stochastic approximation EM (SAEM), which replaces the expectation step of the EM algorithm by one iter ation of a stochastic approximation procedure. The convergence of the SAEM algorithm is established under conditions that are applicable to many pract ical situations. Moreover,it is proved that, under mild additional conditio ns, the attractive stationary points of the SAEM algorithm correspond to th e local maxima of the function. presented to support our findings.