Bayesian density estimation
type: Item
instance of: scholarly article
title: Bayesian density estimation
zbMATH Open document ID: 0898.62048
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/228193
full work available at URL: Ghosh.MAN.html
review text: We describe popular methods of Bayesian density estimation and explore sufficient conditions for the posterior given data to converge to a true underlying distribution \(P_0\) as the data size increases. One of the advantages of Bayesian density estimates is that, unlike classical frequentist methods, choice of the right amount of smoothing is not such a serious problem. Section 2 provides a general background to infinite dimensional problems of inference such as Bayesian nonparametrics, semiparametrics and density estimation. Bayesian nonparametrics has been around for about twenty five years but the other two areas, specially the last, is of more recent vintage. Section 3 indicates in broad terms why different tools are needed for these three different problems and then Section 4 focuses on our main problem of interest, namely, positive posterior consistency results for Bayesian density estimation.
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62G99
zbMATH DE Number: 1184363
zbMATH Keywords: Dirichlet mixtures
zbMATH Keywords: Bayesian nonparametrics
zbMATH Keywords: semiparametrics
zbMATH Keywords: density estimation
zbMATH Keywords: posterior consistency
author: Jayanta K. Ghosh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184363