Dealing with the Multimodal Distributions of Mixture Model Parameters

In a Bayesian analysis of nite mixture models, the symmetry and multi-modality of the posterior distribution of the parameters makes it diicult to interpret or summarize. The common practice of making parameters identii-able by imposing artiicial constraints biases parameter estimates and generally fails to solve the problem of multimodality. We suggest a solution which involves permuting samples from the parameter posterior density so as to remove as much multimodality as possible, and demonstrate its eeectiveness on a simulated example.