Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1], which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein-Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space.
Random Bernstein polynomials
PETRONE, SONIA
1999
Abstract
Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1], which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a "Bernstein-Dirichlet" prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a "changing dimension" parameter space.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
