Markov random field priors for univariate density estimation
Robert L. Wolpert, Michael Lavine · Lecture notes-monograph series · 1996
this paper is to introduce a new parameter + ? 0, set i j p i + , and model explicitly prior beliefs about the nonnegative but otherwise unconstrained vector = ( 0 ; : : : ; k ); of course this induces an implicit prior distribution on the derived quantities p i j i =\\Sigma j . One justification for this artifice is to regard n as the observed value of a random number N of possible observations, and accord N a Poisson prior distribution with parameter + ; the resulting likelihood function for the fp i g is identical to the usual multinomial one. Ferguson's Dirichlet Process can now be recovered by assigning independent Gamma distributions to the f i g, with arbitrary precision (inverse scale) parameter fi ? 0 and shape parameters ff i = ff(I i ) for a nonnegative measure ff(\\Delta) on the Borel sets of R, i