We study the loss of information (measured in terms of the Kullback-Leibler distance) caused by observing "grouped" data (observing only a discretized version of a continuous random variable). We analyze the asymptotical behaviour of the loss of information as the partition becomes finer. In the...

Consider a statistical model, given by the distribution of the observation X, conditional on the parameter [theta], and the prior distribution of the parameter [theta]. Let Hx denote the function that maps the prior mean and the prior covariance matrix into the posterior mean and the posterior...

We present a method for proving finite versions of De Finetti-type theorems for general measurable spaces (). Bernstein operators on the one dimensional simplex [0, 1] are generalized to Bernstein operators on limits of simplices, representing distributions on (). The positivity of finite moment...