Plausible inference from the idea of estimation

TL;DR

This paper proposes a new foundational approach to inference by starting from an estimation operation for magnitudes, which naturally leads to probability rules, offering an alternative to traditional probability axioms.

Contribution

It introduces an estimation-based framework for inference that derives probability rules from basic consistency requirements, providing a novel foundation beyond Cox's axioms.

Findings

Estimation operation leads to probability sum and product rules.

Probability can be derived from estimation principles.

Provides an alternative foundation for Bayesian inference.

Abstract

The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that one can start from an alternative point of view, postulating the existence of an operation for \textit{estimating magnitudes given a state of knowledge}. The properties of this operation can be established through basic consistency requirements. Application of this estimation operation to the truth values of propositions in an integer representation directly yields non-negative, normalized quantities following the sum and product rules of probability.