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...

We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non-parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.

Poisson processes are used in various application fields applications (public health biology, reliability and so on). In their homogeneous version, the intensity process is a deterministic constant. In their inhomogeneous version, it depends on time. To allow for an endogenous evolution of the...

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...

Published nearly seventy years ago, Jeffreys' Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the...

In this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the...

We derive rates of contraction of posterior distributions on non-parametric models resulting from sieve priors. The aim of the study was to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter is, for example,...