Volume 18, Issue 4 e70029
RESEARCH ARTICLE

Testing for the Important Components of Predictive Variance

Dean Dustin

Dean Dustin

First Citizens' Bank, Raleigh, North Carolina, USA

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Souparno Ghosh

Souparno Ghosh

Statistics Department, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

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Bertrand Clarke

Corresponding Author

Bertrand Clarke

Statistics Department, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

Correspondence: Bertrand Clarke ([email protected])

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First published: 17 July 2025

Funding: This work was supported by Leidos, National Cancer Institute, Nebraska Program of Excellence in Computational Science and National Science Foundation (2007418).

ABSTRACT

We give a decomposition of the predictive variance based on the law of total variance by making the response variable dependent on a finite dimensional discrete random variable representing our modeling assumptions. Then, we test which terms in this decomposition are small enough to ignore. This allows us to identify which of the discrete random variables, that is, aspects of modeling, are most important to prediction variance. The terms in the decomposition admit interpretations based on conditional means and variances and are analogous to the terms in a Cochran's theorem decomposition of squared error often used in analysis of variance. Thus, the modeling features are treated as factors in completely randomized design.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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