Widely used parametric generalizedlinear models are, unfortunately,a somewhat limited class of speci � cations. Nonparametric aspects are often introduced to enrich this class, resultingin semiparametricmodels. Focusing on single or k-sample problems,many classical nonparametricapproachesare limited to hypothesistesting. Those that allow estimation are limited to certain functionals of the underlying distributions. Moreover, the associated inference often relies upon asymptotics when nonparametric speci � cations are often most appealing for smaller sample sizes. Bayesian nonparametricapproachesavoid asymptotics but have, to date, been limited in the range of inference. Working with Dirichlet process priors, we overcome the limitations of existing simulation-basedmodel � tting approaches which yield inference that is con � ned to posterior moments of linear functionals of the population distribution.This article provides a computationalapproach to obtain the entire posterior distribution for more general functionals. We illustrate with three applications: investigation of extreme value distributions associated with a single population, comparison of medians in a k-sample problem, and comparison of survival times from different populations under fairly heavy censoring.

Abstract not found

We consider posterior inference in wavelet based models for non-parametric regression with unequally spaced data, density estimation and spectral density estimation. The common theme in all three applications is the lack of posterior independence for the wavelet coe cientsdjk. In contrast, most commonly considered applications of wavelet decompositions in Statistics are based on a setup which implies a posteriori independent coe cients, essentially reducing the inference problem to a series of univariate problems. This is generally true for regression with equally spaced data, image reconstruction, density estimation based on smoothing the empirical distribution, time series applications and deconvolution problems. We propose a hierarchical mixture model as prior probability model on the wavelet coe cients. The model includes a level-dependent positive prior probability mass at zero, i.e., for vanishing coe cients. This implements wavelet coe cient thresholding as a formal Bayes rule. For non-zero coe-cients weintroduce shrinkage by assuming normal priors. Allowing di erent prior variance at each level of detail we obtain level-dependent shrinkage for non-zero coe cients. We implement inference in all three proposed models by a Markov chain Monte Carlo scheme which requires only minor modi cations for the di erent applications. Allowing zero coe cients requires simulation over variable dimension parameter space (Green 1995). We use a pseudo-prior mechanism (Carlin and Chib 1995) to achieve this.

this paper is a simulated annealing algorithm in the sense that we consider increasing powers of the posterior density

Roeder (1990) gives the data set and uses it to exemplify her theoretical results. Here is a brief description. According to the Big Bang theory, matter in the universe expanded at a tremendous rate. Gravitational forces caused the formation of galaxies. Astronomers speculate that gravitational pull led to clustering of galaxies and the research indicates the presence of super-clusters of galaxies surrounded by large voids (stringand-lament pattern). Measurements have recently become available for the distances between our galaxy and others. The distance is estimated by the red shift in the light spectrum in a fashion similar to how the Doppler e ect measures the changes in speed via changes in sound. Under the expansion-universe paradigm, the furthest (from our galaxy) galaxies must be moving at greater velocities, because the distances and velocities are proportional. If, in reality, the galaxies are clumped, the velocities should have amultimodal distribution, each mode corresponding to a cluster. In the region of Corona Borealis the velocities of 82 galaxies were measured. The relative measurement