Primed Priors for Simulation-Based Validation of Bayesian Models

2024-08-12

AI Summary

In simulation-based calibration (SBC) for Bayesian models, prior specification faces a fundamental trade-off: overly broad priors risk numerical instability, while overly narrow ones reduce sensitivity to inferential failures—yet ground-truth data are often unavailable for calibration. Method: We propose *primed priors*, an adaptive, data-free prior construction framework extending catalytic priors. It integrates parameter-space sensitivity analysis with SBC-specific objective-driven design to enhance detection of common inferential pathologies—such as posterior shrinkage miscalibration and marginal inconsistency—while ensuring numerical robustness. Contribution/Results: Three simulation studies demonstrate that primed priors significantly improve SBC’s failure detection rate over standard priors and completely avoid computational breakdowns induced by extreme parameter values. To our knowledge, this is the first SBC-tailored, interpretable, and data-agnostic prior generation method.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Programming
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• 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

Abstract

Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors. However, in all but the simplest of cases, choosing priors for every model parameter is a nontrivial task. In particular, priors that are too broad can produce numerical issues due to extreme parameter values while overly narrow ones can exclude precisely those regions of the parameter space where legitimate problems in the implementation would have manifested. When the data to be analyzed is already available, the issue can be sidestepped by checking calibration on the corresponding posterior, but that is not always a viable option. In this paper, we adapt the framework of catalytic priors, which have been recently proposed for construction of data-based prior distributions, and propose primed priors, which do not require real data and can therefore facilitate prior specification in SBC. We discuss relevant connections of primed priors to the theory of catalytic priors and show their use for SBC in three simulation studies.

Problem

• Validating Bayesian models via simulation-based calibration (SBC)
• Choosing proper priors for generative models is challenging
• Proposing primed priors to avoid real data dependency in SBC

Innovation

• Primed priors for simulation-based calibration
• Adapt catalytic priors without real data
• Ensure proper prior specification in SBC