Open Access
2014 Bayesian methods for the Shape Invariant Model
Dominique Bontemps, Sébastien Gadat
Electron. J. Statist. 8(1): 1522-1568 (2014). DOI: 10.1214/14-EJS933

Abstract

In this paper, we consider the so-called Shape Invariant Model that is used to model a function $f^{0}$ submitted to a random translation of law $g^{0}$ in a white noise. This model is of interest when the law of the deformations is unknown. Our objective is to recover the law of the process $\mathbb{P}_{f^{0},g^{0}}$ as well as $f^{0}$ and $g^{0}$. To do this, we adopt a Bayesian point of view and find priors on $f$ and $g$ so that the posterior distribution concentrates at a polynomial rate around $\mathbb{P}_{f^{0},g^{0}}$ when $n$ goes to $+\infty$. We then derive results on the identifiability of the SIM, as well as results on the functional objects themselves. We intensively use Bayesian non-parametric tools coupled with mixture models, which may be of independent interest in model selection from a frequentist point of view.

Citation

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Dominique Bontemps. Sébastien Gadat. "Bayesian methods for the Shape Invariant Model." Electron. J. Statist. 8 (1) 1522 - 1568, 2014. https://doi.org/10.1214/14-EJS933

Information

Published: 2014
First available in Project Euclid: 8 September 2014

zbMATH: 1297.62069
MathSciNet: MR3263130
Digital Object Identifier: 10.1214/14-EJS933

Subjects:
Primary: 62F15 , 62G05
Secondary: 62G20

Keywords: Bayesian methods , convergence rate of posterior distribution , Grenander’s pattern theory , Non-parametric estimation , Shape invariant model

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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