A unified view on Bayesian varying coefficient models

TL;DR

This paper presents a unified Bayesian framework for varying coefficient models, leveraging penalized complexity priors to ensure coherence, interpretability, and to prevent overfitting across diverse applications.

Contribution

It introduces a coherent prior specification method for varying coefficient models using penalized complexity priors, unifying different application cases.

Findings

Effective in spatial applications with varying coefficients

Provides a coherent interpretation of priors across models

Reduces overfitting through PC priors

Abstract

Varying coefficient models are useful in applications where the effect of the covariate might depend on some other covariate such as time or location. Various applications of these models often give rise to case-specific prior distributions for the parameter(s) describing how much the coefficients vary. In this work, we introduce a unified view of varying coefficients models, arguing for a way of specifying these prior distributions that are coherent across various applications, avoid overfitting and have a coherent interpretation. We do this by considering varying coefficients models as a flexible extension of the natural simpler model and capitalising on the recently proposed framework of penalized complexity (PC) priors. We illustrate our approach in two spatial examples where varying coefficient models are relevant.