A stationary Gaussian process is said to be long-range dependent (resp., anti-persistent) if its spectral density f(λ) can be written as f(λ)=|λ|−2dg(|λ|), where 0d1/2 (resp., −1/2d0), and g is continuous and positive. We propose a novel Bayesian nonparametric approach for the estimation...

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,...

Objective: Pay-for-performance programmes have been widely implemented in primary care, but few studies have investigated their potential adverse effects on the intrinsic motivation of general practitioners (GPs) even though intrinsic motivation may be a key determinant of quality in health...

The article discusses the views of statistics professors Andrew Gelman and Christian P. Robert about the intemperate anti-Bayesian statement appeared on the book of probability theory by mathematician William Feller. It notes that they explore Feller's words along with similar remarks by others...

The missionary zeal of many Bayesians of old has been matched, in the other direction, by an attitude among some theoreticians that Bayesian methods were absurd—not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on...

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...