We give an equivalent of the Bayes risk for a general class of losses in the compact and in the non-compact cases, showing the equivalence with quadratic risks. Some examples are presented.

We are interested in estimating level sets using a Bayesian non-parametric approach, from an independent and identically distributed sample drawn from an unknown distribution. Under fairly general conditions on the prior, we provide an upper bound on the rate of convergence of the Bayesian level...

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...

We have a statistic for assessing an observed data point relative to a statistical model but find that its distribution function depends on the parameter. To obtain the corresponding p-value, we require the minimally modified statistic that is ancillary; this process is called Studentization. We...