True and Pseudo-True Parameters

2026-04-16

AI Summary

When models are misspecified, parameter estimates converge to a pseudo-true value rather than the true parameter, potentially undermining decision relevance. This study investigates the conditions under which the posterior distribution of a Bayesian decision maker concentrates around the pseudo-true value within a linear generalized method of moments framework, and explores the associated decision-theoretic implications. Through asymptotic posterior analysis and robust inference techniques, the work reveals that such posterior concentration is highly sensitive to prior choice and exhibits fragility under misspecification. To address this, the paper proposes a class of simple confidence intervals that guarantee correct average coverage for the true parameter regardless of the degree of misspecification or the form of the prior, thereby offering reliable inference uniformly across all priors.

Technology Category

• Reasoning under Uncertainty: Decision/Utility Theory
• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Imperfect Information

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Parameter estimates in misspecified models converge to pseudo-true parameter values, which minimize a population objective function. Pseudo-true values often differ from quantities of economic interest, raising questions of how, if at all, they are relevant for decision-making. To study this question we consider Bayesian decision-makers facing a linear population minimum distance problem. Within a class of priors motivated by the minimum distance objective, we characterize prior sequences under which posteriors concentrate on the pseudo-true value. This convergence is fragile to small changes in priors, implying that pseudo-true values are relevant for decision-making only in special cases. Constructive results are nevertheless possible in this setting, and we derive simple confidence intervals that guarantee correct average coverage for the true parameter under every prior in the class we study, with no bound on the magnitude of misspecification.

Problem

• misspecified models
• pseudo-true parameters
• Bayesian decision-making
• parameter estimation
• model misspecification

Innovation

• pseudo-true parameters
• model misspecification
• Bayesian decision-making
• minimum distance estimation
• uniform coverage