Bayes Estimation of a Symmetric Unimodal Density via S-Paths
Man-Wai Ho · Journal of Computational and Graphical Statistics · 2006
A Bayes method for a symmetric unimodal density is provided by considering a class of species sampling mixture models containing random densities that are symmetric and unimodal. This class of densities is a generalization of the model considered by an earlier article, in which the Dirichlet process is replaced by a more general class of species sampling models. This article shows that the S-path structure in the earlier model exists analogously in this larger class of models. An explicit characterization of the posterior distribution via a finite mixture of S-paths is derived. This results in a closed-form and tractable Bayes estimator for any symmetric unimodal density as a finite sum over S-paths. This article proposes an extension of the accelerated path sampler, which was originally designed for Dirichlet process mixture models, to approximate this class of estimates. Existence of S-paths in Bayes estimation of a regression problem is discussed. The algorithm again applies. Numerical simulations are given to demonstrate the practicality and the effectiveness of the methodology over other existing methods.