A Bayesian regression framework for circular models with INLA

2026-02-09

AI Summary

This study addresses the limitations of traditional regression models, which employ linear predictor structures and struggle to effectively model circular response variables exhibiting periodicity. The authors propose a novel Bayesian regression framework specifically designed for concentrated circular responses, introducing—for the first time—a probabilistic model that inherently preserves circular characteristics. This framework naturally extends to joint modeling of multiple circular responses and accommodates both linear and circular covariates alongside various random effects. Efficient Bayesian inference is achieved through integrated nested Laplace approximation (INLA), substantially overcoming the modeling constraints imposed by conventional approaches to circular data. Extensive simulations and real-data analyses demonstrate the method’s superior accuracy and practical utility.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

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: Attacks and countermeasures in recommendation systems
• Responsible Web: Consent frameworks and practices on the web

Abstract

Regression models for circular variables are less developed, since the concept of building a linear predictor from linear combinations of covariates and various random effects, breaks the circular nature of the variable. In this paper, we introduce a new approach to rectify this issue, leading to well-defined regression models for circular responses when the data are concentrated. Our approach extends naturally to joint regression models where we can have several circular and non-circular responses, and allow us to handle a mix of linear covariates, circular covariates and various random effects. Our formulation aligns naturally with the integrated nested Laplace approximation (INLA), which provides fast and accurate Bayesian inference. We illustrate our approach through several simulated and real examples.

Problem

• circular regression
• Bayesian inference
• INLA
• circular data
• joint regression models

Innovation

• circular regression
• Bayesian inference
• INLA
• joint modeling
• circular data