Bayesian-Frequentist Hybrid Inference in Applications with Small Sample Sizes

Abstract

The Bayesian-frequentist hybrid model and associated inference can combine the advantages of both Bayesian and frequentist methods and avoid their limitations. However, except for few special cases in existing literature, the computation under the hybrid model is generally nontrivial or even unsolvable. This article develops a computation algorithm for hybrid inference under any general loss functions. Three simulation examples demonstrate that hybrid inference can improve upon frequentist inference by incorporating valuable prior information, and also improve Bayesian inference based on non-informative priors where the latter leads to biased estimates for the small sample sizes used in inference. The proposed method is illustrated in applications including a biomechanical engineering design and a surgical treatment of acral lentiginous melanoma.

KEYWORDS:

• Bayesian analysis
• EM algorithm
• Loss function
• Monte Carlo Markov chain

Supplementary Materials

The supplementary materials include data and MATLAB programs for examples in 4.1, 4.2, 4.3, 5.1, 5.2, as well as a user manual.

Acknowledgments

The authors thank the reviewer and the associate editor for their constructive comments that have significantly improved this article.

Disclosure Statement

The authors report there are no competing interests to declare.