Bayesian confidence estimation: an alternative approach

From a Bayesian point of wiew, 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