The Median Probability Model and Correlated Variables

Understand

The median probability model (MPM) Barbieri and Berger (2004) is defined as the model consisting of those variables whose marginal posterior probability of inclusion is at least 0.5.

• The MPM rule yields the best single model for prediction in orthogonal and nested correlated designs.
• This result was originally conceived under a specific class of priors, such as the point mass mixtures of non-informative and g-type priors.
• The MPM rule, however, has become so very popular that it is now being deployed for a wider variety of priors and under correlated designs, where the properties of MPM are not yet completely understood.