Bayesian density estimation
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.
scientific article; zbMATH DE number 1184363