BAYESIAN CONFIDENCE ESTIMATION - AN ALTERNATIVE APPROACH

From a Bayesian point of view, the estimation of an unknown parameter can be interpreted (in many situations) as the problem of fixing a partition of the parameter space (by means of small intervals I1,...,I(k)) and choosing an interval I(j) from this partition, provided that sufficient information has been obtained. This idea is developed in a decision theory setting. If the Kolmogorov-Smirnov loss is used, it is proved that I(j) is the best interval estimation if and only if its posterior probability is greater than or equal to 1/2.