Continuum-state hidden Markov models with dirichlet state distributions

In some modeling scenarios, particularly those representing data from natural sources, the discrete states conventionally used in hidden Markov models (HMMs) are at best an approximation, since the discrete states are a modeling artifact. In this paper we present an HMM in which the states take any value in a simplex. The Dirichlet distribution is used to provide a parsimonious representation of the distribution of the states. Conditional state estimates using an extension of the conventional forward/backward method, using Dirichlet distributions to provide a nearly closed-form, but approximate, representation.