An alternative inference tool to total probability formula and its applications

TL;DR

This paper introduces a novel inference tool based on median for Bayesian statistics, offering improvements over traditional total probability and Bayes formulas, with potential extensions to broader areas of probability and statistics.

Contribution

It presents a new median-based total probability formula and demonstrates its applications, filling a gap in existing statistical inference methods.

Findings

Median-based total probability formula defined and its properties proved

Applications show improved inference results

Potential for extension to other probability and statistics areas

Abstract

Total probability and Bayes formula are two basic tools for using prior information in the Bayesian statistics. In this paper we introduce an alternative tool for using prior information. This new toold enables us to improve some traditional results in statistical inference. However, as far as the authors know, there is no work on this subject, except [1]. The results of this paper can be extended to other branches of probability and statistics. In Section 2 total probability formula based on median is defined and its basic properties are proved. A few applications of this new tool are given in Section 3.