Assessing the Role of Bayesian Decision Theory in Optimal Statistical Inference and Risk Minimization

Posted: May 05, 2017

• Eleanor Butler
• Elena Scott
• Eli Ward

Abstract

Bayesian decision theory represents a fundamental framework for statistical inference that integrates probability theory with decision-making under uncertainty. The classical approach to statistical inference has traditionally been dominated by frequentist methods, which often rely on asymptotic properties and repeated sampling principles. However, these methods frequently encounter limitations in practical applications where prior information is available, sample sizes are limited, or decisions must be made sequentially. The Bayesian paradigm offers a coherent alternative that naturally incorporates prior knowledge and provides a unified approach to estimation, prediction, and decision-making.