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Random Bernstein Polynomials
Author(s) -
Petrone Sonia
Publication year - 1999
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00155
Subject(s) - mathematics , bernstein polynomial , dirichlet distribution , dirichlet process , polynomial , probability distribution , bayesian probability , mathematical analysis , statistics , boundary value problem
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.