Practical Robust Estimators for the Imprecise Dirichlet Model

TL;DR

This paper develops efficient methods for computing robust and credible interval estimates within the Imprecise Dirichlet Model, enhancing practical uncertainty quantification for categorical data.

Contribution

It introduces exact, conservative, and approximate interval estimation techniques for the IDM applicable to various statistical estimators, including entropy and mutual information.

Findings

Provides exact and approximate interval estimation methods

Enhances practical applicability of the IDM

Improves uncertainty quantification for categorical data

Abstract

Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or intervals. The main objective of this work is to derive exact, conservative, and approximate, robust and credible interval estimates under the IDM for a large class of statistical estimators, including the entropy and mutual information.