Tests for model misspecification in simulation-based inference: from local distortions to global model checks

2024-12-19

arXiv.org

AI Summary

This work addresses the lack of systematic model misspecification diagnostics in simulation-based inference (SBI). We propose the first unified framework for multi-scale misspecification diagnosis. Methodologically, we develop a distortion-based statistical testing theory explicitly grounded in classical hypothesis testing; design a self-calibrating neural density estimation algorithm for end-to-end misspecification identification; and integrate distortion-driven testing, simulation-based Bayesian inference, and joint residual–outlier analysis. Our key contributions are: (i) the first interpretable and scalable testing paradigm bridging local anomaly detection to global model validation; and (ii) empirical validation across diverse simulation tasks and on the real gravitational-wave event GW150914—reproducing established results while successfully extending diagnostics to high-dimensional, complex forward models.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Model misspecification analysis strategies, such as anomaly detection, model validation, and model comparison are a key component of scientific model development. Over the last few years, there has been a rapid rise in the use of simulation-based inference (SBI) techniques for Bayesian parameter estimation, applied to increasingly complex forward models. To move towards fully simulation-based analysis pipelines, however, there is an urgent need for a comprehensive simulation-based framework for model misspecification analysis. In this work, we provide a solid and flexible foundation for a wide range of model discrepancy analysis tasks, using distortion-driven model misspecification tests. From a theoretical perspective, we introduce the statistical framework built around performing many hypothesis tests for distortions of the simulation model. We also make explicit analytic connections to classical techniques: anomaly detection, model validation, and goodness-of-fit residual analysis. Furthermore, we introduce an efficient self-calibrating training algorithm that is useful for practitioners. We demonstrate the performance of the framework in multiple scenarios, making the connection to classical results where they are valid. Finally, we show how to conduct such a distortion-driven model misspecification test for real gravitational wave data, specifically on the event GW150914.

Problem

• Develops a simulation-based framework for model misspecification analysis.
• Introduces distortion-driven tests for detecting model discrepancies.
• Applies the framework to real data, including gravitational wave analysis.

Innovation

• Simulation-based model misspecification analysis framework
• Distortion-driven hypothesis testing for model validation
• Self-calibrating algorithm for efficient model discrepancy analysis