Revisiting the Lost Submarine Problem: A Decision Theoretic Approach

TL;DR

This paper revisits the lost submarine problem to demonstrate that a decision theoretic approach clarifies the purpose of confidence intervals, leading to optimal solutions tailored to specific inference goals.

Contribution

It introduces a decision theoretic framework to resolve issues with confidence intervals and shows how different purposes require different optimal statistical procedures.

Findings

Decision theoretic approach clarifies confidence interval interpretation

Different inference purposes lead to distinct optimal procedures

A single optimal choice emerges for each well-defined purpose

Abstract

This article includes a discussion of the ``lost submarine problem", following Morey \emph{et al} (2016). As the title of that paper suggests (\emph{The fallacy of placing confidence in confidence intervals}), the example is intended to illustrate the futility of relying on the confidence interval as a formal inference statement. In the view of this author, the misgivings expressed in Morey \emph{et al} (2016) can be resolved using a decision theoretic approach. While it is true that a variety of statistical methods lead to a variety of confidence intervals, once we precisely define their purpose, a single optimal choice emerges. Furthermore, distinct purposes lead to distinct optimal choices. Therefore, that a variety of procedures exist is an advantage rather than a liability.