Bayes procedures for adaptive inference in inverse problems for the white noise model

Autor:	Knapik, B. T., Szabó, B. T., van der Vaart, A. W., van Zanten, J. H.
Rok vydání:	2012
Předmět:	Mathematics - Statistics Theory 62G05 62C15 (Primary) 62G20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic "smoothness", without using knowledge about this regularity. Both methods are illustrated by simulation examples. Comment: 41 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1209.3628 Zobrazit plný text záznamu View this record from Arxiv