On choosing mixture components via non-local priors

Understand

Choosing the number of mixture components remains an elusive challenge.

• Model selection criteria can be either overly liberal or conservative and return poorly-separated components of limited practical use.
• We formalize non-local priors (NLPs) for mixtures and show how they lead to well-separated components with non-negligible weight, interpretable as distinct subpopulations.
• We also propose an estimator for posterior model probabilities under local and non-local priors, showing that Bayes factors are ratios of posterior to prior empty-cluster probabilities.