The Third Way Of Probability & Statistics: Beyond Testing and Estimation To Importance, Relevance, and Skill

TL;DR

This paper advocates for a third approach in probability and statistics focused on making observable-based statements, emphasizing relevance and verification over traditional testing and estimation methods.

Contribution

It introduces the logical probability approach that replaces hypothesis testing and parameter estimation with observable-based statements and emphasizes model verification.

Findings

Eliminates reliance on hypothesis testing and Bayes factors.

Promotes models based on relevance and importance for decision-making.

Requires models to be publicly verifiable and undergo verification.

Abstract

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation. The Third Way is the logical probability approach, which is to make statements $\Pr(Y \in y | X,D,M)$ about observables of interest $Y$ taking values $y$, given probative data $X$, past observations (when present) $D$ and some model (possibly deduced) $M$. Significance and the false idea that probability models show causality are no more, and in their place are importance and relevance. Models are built keeping on information that is relevant and important to a decision maker (and not a statistician). All models are stated in publicly verifiable fashion, as predictions. All models must undergo a verification process before any trust is put into them.