Open Journal of Statistics

Volume 13, Issue 2 (April 2023)

ISSN Print: 2161-718X   ISSN Online: 2161-7198

Google-based Impact Factor: 1.45  Citations  

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

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DOI: 10.4236/ojs.2023.132010    240 Downloads   1,022 Views  

ABSTRACT

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

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Santis, F. and Gubbiotti, S. (2023) Bayesian Set Estimation with Alternative Loss Functions: Optimality and Regret Analysis. Open Journal of Statistics, 13, 195-211. doi: 10.4236/ojs.2023.132010.

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