Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis

Decision-theoretic interval estimation requires the use of loss functions that, typically, take into account size and coverage sets. We here consider class monotone under quite general conditions, guarantee Bayesian optimality highest posterior probability focus on three specific families losses, namely linear, exponential rational losses whose difference consists in way sizes sets are penalized. Within standard yet important set-up a normal model we propose: 1) an analysis, to compare solutions yielded by alternative classes losses; 2) regret evaluate additional non-optimal intervals fixed credibility. The article uses application clinical trial as illustrative example.