M. Barbieri, E. George, V. Rockova, J. Berger
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 applied for a specific class of priors, such as the point mass mixtures of non-informative and g-type priors. The MPM rule, however, 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. In this work we shed light on properties of MPM by characterizing situations when MPM is still safe under correlated designs and providing significant generalizations to a broader class of priors (such as continuous spike-and-slab priors). We also provide new supporting evidence for the suitability of g-priors, as opposed to independent product priors, using new predictive matching arguments.
Keywords: Bayesian variable selection, median probability model, multicollinearity, Spike and slab
Scheduled
GT8-3 Bayesian Inference
September 4, 2019 2:45 PM
I2L7. Georgina Blanes building