Most probable explanation (MPE)
Introduction
Most probable explanation (MPE), also known as max propagation, computes the most probable configuration of variables that do not have evidence.
When the Most probable explanation (MPE) option is used, probabilities for discrete variables may not sum to 1. This is expected behavior.
The difference between standard inference and MPE inference, is that when variables are marginalized out from distributions in order to compute queries, instead of summing values, the maximum is used.
The likelihood/log-likelihood returned when the MPE option is used, equals the likelihood/log-likelihood that would be returned, if the most probable configuration found, was entered as evidence.
Dynamic Bayesian networks
When used with dynamic Bayesian networks (time series models), MPE can be used to calculate the most probable sequence. The process is analogous to the Viterbi algorithm used with Hidden Markov Models, although dynamic Bayesian networks can represent a wider class of models than Hidden Markov models.