Multiset Model Selection

ABSTRACT

Model selection algorithms are required to efficiently traverse the space of models. In problems with high-dimensional and possibly correlated covariates, efficient exploration of the model space becomes a challenge. To overcome this, a multiset is placed on the model space to enable efficient exploration of multiple model modes with minimal tuning. The multiset model selection (MSMS) framework is based on independent priors for the parameters and model indicators on variables. Posterior model probabilities can be easily obtained from multiset averaged posterior model probabilities in MSMS. The effectiveness of MSMS is demonstrated for linear and generalized linear models. Supplementary material for this article is available online.

KEYWORDS:

• Bayesian modeling
• MCMC
• Variable selection

Supplementary Materials

The supplemental materials contain derivations of the normalizing constant for the multisite model and a derivation of multisite probabilities for cases where k is greater than 2.