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.

摘要

贝叶斯-频率论混合模型和关联推理可以结合贝叶斯和频率论方法的优点并避免它们的局限性。然而，除了现有文献中的少数特殊情况外，混合模型下的计算通常是不平凡的，甚至是无解的。本文开发了一种在任何一般损失函数下进行混合推理的计算算法。三个模拟示例表明，混合推理可以通过合并有价值的先验信息来改进频率论推理，还可以改进基于非信息先验的贝叶斯推理，后者会导致对推理中使用的小样本量的估计有偏差。所提出的方法在包括生物力学工程设计和肢端黑色素瘤的手术治疗在内的应用中得到了说明。