Dirichlet process mixture models with multiple modalities

The Dirichlet process can be used as a nonparametric prior for an infinite-dimensional probability mass function on the parameter space of a mixture model. The set of parameters over which it is defined is generally used for a single, parametric distribution. We extend this idea to parameter spaces that characterize multiple distributions, or modalities. In this framework, observations containing multiple, incompatible pieces of information can be mixed upon, allowing for all information to inform the final clustering result. We provide a general MCMC sampling scheme and demonstrate this framework on a Gaussian-HMM mixture model applied to synthetic and Major League Baseball data.