2013/08/25 by Abhra Sarkar, Sarkar, Abhra, Debdeep Pati +5
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1308.5427
openalex publication_date 2013/08/25 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Bayesian density deconvolution using nonparametric prior distributions is a\nuseful alternative to the frequentist kernel based deconvolution estimators due\nto its potentially wide range of applicability, straightforward uncertainty\nquantification and generalizability to more sophisticated models. This article\nis the first substantive effort to theoretically quantify the behavior of the\nposterior in this recent line of research. In particular, assuming a known\nsupersmooth error density, a Dirichlet process mixture of Normals on the true\ndensity leads to a posterior convergence rate same as the minimax rate (\log\nn)-\η/\β adaptively over the smoothness \η of an appropriate\nH "older space of densities, where \β is the degree of smoothness of the\nerror distribution. Our main contribution is achieving adaptive minimax rates\nwith respect to the Lp norm for 2 \≤ p \≤ \∞ under mild regularity\nconditions on the true density. En route, we develop tight concentration bounds\nfor a class of kernel based deconvolution estimators which might be of\nindependent interest.\n