Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors

TLDR

The paper introduces a new concept for constructing prior distributions. The method exploits the nested structure of model components, defining priors that penalize deviations from a base model using a user‑defined scaling parameter in both univariate and multivariate settings. The priors are invariant to reparameterisations, naturally linked to Jeffreys’ priors, support Occam’s razor, exhibit strong robustness, and the authors demonstrate their suitability through examples and theory.

Abstract

In this paper, we introduce a new concept for constructing prior distributions. We exploit the natural nested structure inherent to many model components, which defines the model component to be a flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.