An objective non-local prior for skew-symmetric models

2026-03-09

AI Summary

This study addresses the lack of an objective, hyperparameter-free nonlocal prior for symmetry testing by proposing a bias-based objective nonlocal prior. The method automatically constructs a weakly informative prior intrinsically linked to the model structure by assigning a uniform distribution to the shape parameter of a family of skewed-symmetric models, thereby eliminating the need for user-specified hyperparameters. Within a Bayesian hypothesis testing framework and using the skew-normal model, the proposed approach substantially enhances both the automation and robustness of symmetry tests. Simulation studies and real data analyses demonstrate that the prior effectively evaluates the normality assumption and exhibits superior practical performance.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose an objective non-local prior for testing symmetry against skew-symmetric alternatives. The prior is derived through a formal construction rule by assigning a uniform distribution to a discrepancy-based measure of the shape parameter's effect. This approach avoids the need for user-specified hyperparameters and produces a weakly informative prior tailored to the skew-symmetric family. We illustrate the use of the proposed prior in the context of testing normality against skew-normal alternatives through both a simulation study and a real-data application.

Problem

• skew-symmetric models
• objective prior
• non-local prior
• symmetry testing
• shape parameter

Innovation

• objective non-local prior
• skew-symmetric models
• symmetry testing
• weakly informative prior
• discrepancy-based measure