Bayesian methods in the Shape Invariant Model (I): Posterior contraction rates on probability measures

2013/02/08 by Dominique Bontemps, Bontemps, Dominique, Sébastien Gadat +2
Computer Science · Mathematics · #62F15 #62G05 #62G20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62F15 #msc:62G05 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.1302.2043

36 pages

openalex publication_date 2013/02/08 · arxiv created 2013/03/12 · arxiv updated 2013/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the deformations is unknown. We aim to recover the law of the process P(f0,g0). In this perspective, we adopt a Bayesian point of view and find prior on f and g such that the posterior distribution concentrates at a polynomial rate around P(f0,g0) when n goes to infinity. We intensively use some Bayesian non parametric tools coupled with mixture models and believe that some of our results obtained on this mixture framework may be also of interest for frequentist point of view.

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