Wasserstein complexity penalization priors: a new class of penalizing complexity priors

Abstract

Penalizing complexity (PC) priors provide a principled framework for reducing model complexity by penalizing the Kullback--Leibler Divergence (KLD) between a ``simple'' base model and a more complex model. However, constructing priors by penalizing the KLD becomes impossible in many cases because the KLD is infinite, and alternative principles often lose interpretability in terms of KLD. We propose a new class of priors, the Wasserstein complexity penalization (WCP) priors, which replace the KLD with the Wasserstein distance in the PC prior framework. WCP priors avoid the issue of infinite model distances and retain interpretability by adhering to adjusted principles. Additionally, we introduce the concept of base measures, removing the parameter dependency on the base model, and extend the framework to joint WCP priors for multiple parameters. These priors can be constructed analytically and we have both analytical and numerical implementations in R programming language. We demonstrate their use in previous PC prior applications and as well as new multivariate settings.