Penalising model component complexity: A principled, practical approach to constructing priors

TL;DR

This paper proposes a new method for constructing priors based on penalising model component complexity, leveraging nested structures to create robust, reparameterisation-invariant priors that support Occam's razor.

Contribution

It introduces a novel class of priors that penalise complexity relative to base models, with theoretical justification and practical examples demonstrating their effectiveness.

Findings

Priors are invariant to reparameterisations.

They support Occam's razor and show robustness.

Applicable to univariate and multivariate models.

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.