Estimation of mixture densities for the classical Gaussian compound decision problem and their associated (empirical) Bayes rules is considered from two new perspectives. The first, motivated by Brown and Greenshtein, introduces a nonparametric maximum likelihood estimator of the mixture density...

Hansen, Kooperberg and Sardy introduced a family of continuous, piecewise linear functions defined over adaptively selected triangulations of the plane as a general approach to statistical modelling of bivariate densities and regression and hazard functions. These "triograms" enjoy a natural...

For an arbitrary subselection of the identities defining the stochastic independence (of several events), there exist random events, with prescribed probabilities, satisfying only the identities from the subselection. A similar statement holds if the events are required to be exchangeable.