We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that...

We consider finite state space stationary hidden Markov models (HMMs) in the situation where the number of hidden states is unknown. We provide a frequentist asymptotic evaluation of Bayesian analysis methods. Our main result gives posterior concentration rates for the marginal densities, that...

The choice of the summary statistics in Bayesian inference and in particular in ABC algorithms is paramount to produce a valid outcome. We derive necessary and sufficient conditions on those statistics for the corresponding Bayes factor to be convergent, namely to asymptotically select the true...

The issue of using informative priors for estimation of mixtures at multiple time points is examined. Several different informative priors and an independent prior are compared using samples of actual and simulated aerosol particle size distribution (PSD) data. Measurements of aerosol PSDs refer...

Empirical Bayes methods are often thought of as a bridge between classical and Bayesian inference. In fact, in the literature the term empirical Bayes is used in quite diverse contexts and with different motivations. In this article, we provide a brief overview of empirical Bayes methods...

Empirical Bayes procedures are commonly used based on the supposed asymptotic equivalence with fully Bayesian procedures, which, however, has not so far received full theoretical support in terms of uncertainty quantification. In this note, we provide some results on contraction rates of...

We present a dependent Bayesian nonparametric model for the proba- bilistic modelling of species-by-site data, i.e. population data where observations at different sites are classified into distinct species. We use a dependent version of the Griffiths-Engen-McCloskey distribution, the...

Although there have been a lot of developpements in the recent years on estimation in Bayesian nonparametric models, from a theoretical point view as well as from a methodological point of view, little has been done on Bayesian testing in nonparametric frameworks. In this talk I will be...

In this paper we derive adaptive non-parametric rates of concentration of the posterior distributions for the density model on the class of Sobolev and Besov spaces. For this purpose, we build prior models based on wavelet or Fourier expansions of the logarithm of the density. The prior models...

The original Studentization was the conversion of a sample mean departure into the familiar t-statistic, plus the derivation of the corresponding Student distribution function; the observed value of the distribution function is the observed p-value, as presented in an elemental form. We examine...