Canonical representations for dependent Dirichlet populations
Seminar Room 1, Newton Institute
A wide class of Markov processes having a Ferguson-Dirichlet stationary measure is characterized by solving the following problem: fix the eigenfunctions of the generator to be orthogonal polynomials; how do all possible eigenvalues look like? Such a representation reveals a strong connection with the classical Lancaster problem of finding the correlation structure of bivariate distributions with fixed marginals. A similar representation is shown to hold for processes on the discrete simplex with Multinomial-Dirichlet stationary measure. The connection between the two classes of stochastic processes has a strong Bayesian flavour, which stems from a probabilistic derivation of all Multivariate orthogonal polynomials involved.