Penalizing complexity priors for Bayesian inference of circular models

TL;DR

This paper introduces Penalized Complexity priors for Bayesian circular models, addressing prior selection challenges and providing a framework for simpler model contraction in directional data analysis.

Contribution

It develops PC priors specifically for circular distributions, filling a theoretical gap and offering practical comparisons with existing hyperpriors.

Findings

PC priors effectively contract to simpler models in circular scenarios

Simulation studies show improved prior performance over existing methods

Case study demonstrates practical applicability of the proposed priors

Abstract

Advancements in computational power and methodologies have enabled research on massive datasets. However, tools for analyzing data with directional or periodic characteristics, such as wind directions and customers' arrival time in 24-hour clock, remain underdeveloped. While statisticians have proposed circular distributions for such analyses, significant challenges persist in constructing circular statistical models, particularly in the context of Bayesian methods. These challenges stem from limited theoretical development and a lack of historical studies on prior selection for circular distribution parameters. In this article, we propose a framework for selecting hyperpriors that contracts to a simpler model in circular scenarios, especially when there is insufficient information to guide prior selection. We introduce well-examined Penalized Complexity (PC) priors for the most widely used circular distributions. Comprehensive comparisons with existing hyperpriors in the literature are conducted through simulation studies and a practical case study. Finally, we discuss the contributions and implications of our work, providing a foundation for further advancements in constructing Bayesian circular statistical models.