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Understanding Peelle's Pertinent Puzzle bias in generalized least squares regression through eigenspectrum analysis
Noah A W Walton1,2, William N Fritsch3, Amanda M Lewis4,3
1Los Alamos National Laboratory, Los Alamos, 87545, NM, USA. nwalton@lanl.gov.
Scientific Reports
|November 19, 2025
Summary
Peele's Pertinent Puzzle (PPP) bias in generalized least squares (GLS) regression arises from specific data covariance matrix (DCM) correlations. A new framework uses eigenspectrum analysis to understand and generalize this bias, offering solutions for experimental data analysis.
Area of Science:
- Nuclear data evaluation
- Statistical modeling
- Experimental physics
Background:
- Generalized least squares (GLS) regression is sensitive to correlation structures within the data covariance matrix (DCM).
- Peele's Pertinent Puzzle (PPP) describes a known bias in nuclear data evaluation stemming from these DCM correlations.
Purpose of the Study:
- To introduce a generative, forward modeling framework for characterizing the PPP bias.
- To generalize the understanding of PPP beyond nuclear data.
- To identify conditions and data types susceptible to this bias.
Main Methods:
- Eigenspectrum analysis of the data covariance matrix (DCM).
- Generative, forward modeling framework development.
- Adaptation of pre-whitening cross-validation techniques.
Main Results:
- The eigenspectrum analysis reveals the root cause of the PPP bias.
- The framework demonstrates that PPP can affect any experimental data with quantified systematic uncertainties, such as neutron time-of-flight data.
- The study provides insights into the specific regimes where the bias is most likely to occur.
Conclusions:
- The proposed framework offers a generalized approach to understanding and mitigating bias in GLS regression.
- The findings are applicable to a broader range of experimental sciences beyond nuclear data evaluation.
- Modified cross-validation methods can incorporate corrections for the PPP bias.
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