Bayesian confidence intervals with more power to estimate the minimum effect and determine the sign

Abstract

In this article, we propose two confidence intervals (CIs) for a single parameter, which can represent an effect in practice, through a Bayesian decision theoretic approach for different goals. One balances length and separating zero from a CI. The other one balances length and the ability of making direction decision of a CI. Two loss functions are constructed by adding suitable penalty terms into the traditional loss function. Then two CIs are obtained by minimizing the loss functions. When compared with the traditional Bayesian CI, the first CI has more chance to estimate the minimum effect; the second CI has more chance to make directional decision for the parameter. General steps for minimizing the loss functions to obtain the CIs are provided. A real data are analyzed through constructing the second CI.

KEYWORDS:

• Confidence interval
• loss function
• posterior expectation
• directional decision