Statistical Science

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

Daniel Simpson, Håvard Rue, Andrea Riebler, Thiago G. Martins, and Sigrunn H. Sørbye

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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.

Article information

Statist. Sci. Volume 32, Number 1 (2017), 1-28.

First available in Project Euclid: 6 April 2017

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Bayesian theory interpretable prior distributions hierarchical models disease mapping information geometry prior on correlation matrices


Simpson, Daniel; Rue, Håvard; Riebler, Andrea; Martins, Thiago G.; Sørbye, Sigrunn H. Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statist. Sci. 32 (2017), no. 1, 1--28. doi:10.1214/16-STS576.

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See also

Supplemental materials

  • Supplement to “Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors”. The supplementary material contains the proofs of all theorems contained in the paper. It also contains a detailed description of the Student $t$-simulation study used in Section 3.4. The R-code for analysing all examples and generating the corresponding figures in this report, is available at