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
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
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