Hypotheses testing and posterior concentration rates for semi-Markov processes
Statistics Theory
2019-06-14 v1 Statistics Theory
Abstract
In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and finite state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.
Cite
@article{arxiv.1906.05566,
title = {Hypotheses testing and posterior concentration rates for semi-Markov processes},
author = {V Barbu and Ghislaine Gayraud and N. Limnios and I. Votsi},
journal= {arXiv preprint arXiv:1906.05566},
year = {2019}
}