Sensitivity Analysis of Classical and Conditional Bayesian Problems of Many Hypotheses Testing

Abstract

The problem of choosing the loss function in the Bayesian problem of many hypotheses testing is considered. It is shown that linear and quadratic loss functions are the most-used ones. For any kind of loss function, the risk function in the Bayesian problem of many hypotheses testing contains the errors of two kinds. The Bayesian decision rule minimizes the total effect of these errors. The share of each of them in the optimal value of risk function is unknown. When solving many important problems, the results caused by different errors significantly differ from each other. Therefore, it is necessary to guarantee the limitation on the most undesirable kind of these errors and to minimize the errors of the second kind. For solving these problems, this article are states and solves conditional Bayesian tasks of testing many hypotheses. The results of sensitivity analysis of the classical and conditional Bayesian problems are given and their advantages and drawbacks are considered.

Keywords:

• Bayesian approach
• Conditional Bayesian task
• Loss function
• Risk function
• Sensitivity analysis

Mathematics Subject Classification:

• 62F15
• 62F03

Notes

(continued)