If the distribution P is considered random and distributed according to , as it is in Bayesian inference, then the posterior distribution is the conditional distribution of P given the observations.â€¦ (More)

Mixture models for density estimation provide a very useful set up for the Bayesian or the maximum likelihood approach. For a density on the unit interval, mixtures of beta densities form a flexibleâ€¦ (More)

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior distribution in density estimation problems, where the densities are location or location-scale mixtures ofâ€¦ (More)

Here we review the role of the Dirichlet process and related prior distribtions in nonparametric Bayesian inference. We discuss construction and various properties of the Dirichlet process. We thenâ€¦ (More)

This article describes a Bayesian approach to estimating the spectral density of a stationary time series. A nonparametric prior on the spectral density is described through Bernstein polynomials.â€¦ (More)

Abstract: We consider nonparametric Bayesian estimation of a probability density p based on a random sample of size n from this density using a hierarchical prior. The prior consists, for instance,â€¦ (More)

Exponential families arise naturally in statistical modelling and the maximum likelihood estimate (MLE) is consistent and asymptotically normal for these models [Berk [2]]. In practice, often oneâ€¦ (More)

We consider the problem of testing monotonicity of the regression function in a nonparametric regression model. We introduce test statistics that are functionals of a certain natural U-process. Weâ€¦ (More)

We present a flexible framework for predicting error measures in multiple testing situations under dependence. Our approach is based on modeling the distribution of the probit transform of theâ€¦ (More)

We study consistency and asymptotic normality of posterior distributions of the regression coeecient in a linear model when the dimension of the parameter grows with the sample size. Under certainâ€¦ (More)