We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a...

This introduction to Bayesian statistics presents themain concepts as well as the principal reasons advocatedin favour of a Bayesian modelling. We coverthe various approaches to prior determination as wellas the basis asymptotic arguments in favour of usingBayes estimators. The testing aspects...

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

This chapter provides a overview of Bayesian inference, mostly emphasising that it is auniversal method for summarising uncertainty and making estimates and predictions usingprobability statements conditional on observed data and an assumed model (Gelman 2008).The Bayesian perspective is thus...