Using wavelet thresholding methods, we give an adaptive estimator of [theta]=[integral operator]f2, where f is coming from the white noise model. We estimate the random bias term, which is the dominating term in the decomposition of the quadratic error, and state a central limit theorem. This...

Abstract For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin´s recent book,...

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...

type="main" xml:id="rssb12056-abs-0001" <title type="main">Summary</title> <p>The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used...</p>