### Abstract

The expected auxiliary variable method is a general framework for Monte Carlo simulation in situations where quantities of interest are untractable and prevent the implementation of classical methods. The method finds application in situations where marginal computations are of interest, transdimensional move design is difficult in model selection setups, when the normalising constant of a particular distribution is unknown but required for exact computations. I will present several examples of applications of this principle as well as some theoretical results that we have recently obtained in some specific scenarios.