Subhashis Ghosal

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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. The prior is, of course, a measure on some σ-field on and we must assume that the expressions in the display are well defined. In particular, we assume that the(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 of normal distributions with the scale parameter lying between two positive numbers. The true density is also assumed to lie in this class with the true mixing(More)
We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the posterior measure relative to distances derived from a testing criterion. We then specialize our results to independent,(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. Because the actual likelihood is very complicated, a pseudoposterior distribution is obtained by updating the prior using the Whittle likelihood. A Markov chain(More)
We consider the problem of estimating the mean of an infinitedimensional normal distribution from the Bayesian perspective. Under the assumption that the unknown true mean satisfies a “smoothness condition,” we first derive the convergence rate of the posterior distribution for a prior that is the infinite product of certain normal distributions and compare(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 one needs to consider models with a large number of parameters, particularly if the sample size is large; see Huber [14], Haberman [13] and Portnoy [18 21]. One may(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. We study the limiting distribution of these test statistics through strong approximation methods and the extreme value theory for Gaussian processes. We show that(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, of prior weights on the regularity of the unknown density combined with priors that are appropriate given that the density has this regularity. More generally,(More)