Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (original) (raw)
February 2017 Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
Daniel Simpson,Håvard Rue,Andrea Riebler,Thiago G. Martins,Sigrunn H. Sørbye
Statist. Sci. 32(1): 1-28 (February 2017). DOI: 10.1214/16-STS576
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.
Citation
Daniel Simpson. Håvard Rue. Andrea Riebler. Thiago G. Martins. Sigrunn H. Sørbye. "Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors." Statist. Sci. 32 (1) 1 - 28, February 2017. https://doi.org/10.1214/16-STS576
Information
Published: February 2017
First available in Project Euclid: 6 April 2017
Digital Object Identifier: 10.1214/16-STS576
Keywords: Bayesian theory, disease mapping, hierarchical models, information geometry, interpretable prior distributions, prior on correlation matrices
Rights: Copyright © 2017 Institute of Mathematical Statistics
Vol.32 • No. 1 • February 2017
