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

Handle URI:
http://hdl.handle.net/10754/623413
Title:
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
Authors:
Simpson, Daniel; Rue, Haavard ( 0000-0002-0222-1881 ) ; Riebler, Andrea; Martins, Thiago G.; Sørbye, Sigrunn H.
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 repa-rameterisations, 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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Simpson D, Rue H, Riebler A, Martins TG, Sørbye SH (2017) Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statistical Science 32: 1–28. Available: http://dx.doi.org/10.1214/16-STS576.
Publisher:
Institute of Mathematical Statistics
Journal:
Statistical Science
Issue Date:
6-Apr-2017
DOI:
10.1214/16-STS576
Type:
Article
ISSN:
0883-4237
Sponsors:
The authors are grateful to the Editor, Associate Editor and three anonymous referees for exceptionally helpful and constructive reports. The authors acknowledge Gianluca Baio, Haakon C. Bakka, Simon Barthelmé, Joris Bierkens, Sylvia Frühwirth-Schnatter, Geir-Arne Fuglstad, Nadja Klein, Thomas Kneib, Alex Lenkoski, Finn K. Lindgren, Christian P. Robert and Malgorzata Roos for stimulating discussions and comments related to this work.
Additional Links:
http://projecteuclid.org/euclid.ss/1491465621
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSimpson, Danielen
dc.contributor.authorRue, Haavarden
dc.contributor.authorRiebler, Andreaen
dc.contributor.authorMartins, Thiago G.en
dc.contributor.authorSørbye, Sigrunn H.en
dc.date.accessioned2017-05-09T08:34:34Z-
dc.date.available2017-05-09T08:34:34Z-
dc.date.issued2017-04-06en
dc.identifier.citationSimpson D, Rue H, Riebler A, Martins TG, Sørbye SH (2017) Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors. Statistical Science 32: 1–28. Available: http://dx.doi.org/10.1214/16-STS576.en
dc.identifier.issn0883-4237en
dc.identifier.doi10.1214/16-STS576en
dc.identifier.urihttp://hdl.handle.net/10754/623413-
dc.description.abstractIn 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 repa-rameterisations, 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.en
dc.description.sponsorshipThe authors are grateful to the Editor, Associate Editor and three anonymous referees for exceptionally helpful and constructive reports. The authors acknowledge Gianluca Baio, Haakon C. Bakka, Simon Barthelmé, Joris Bierkens, Sylvia Frühwirth-Schnatter, Geir-Arne Fuglstad, Nadja Klein, Thomas Kneib, Alex Lenkoski, Finn K. Lindgren, Christian P. Robert and Malgorzata Roos for stimulating discussions and comments related to this work.en
dc.publisherInstitute of Mathematical Statisticsen
dc.relation.urlhttp://projecteuclid.org/euclid.ss/1491465621en
dc.rightsArchived with thanks to Statistical Scienceen
dc.subjectBayesian theoryen
dc.subjectinterpretable prior distributionsen
dc.subjecthierarchical modelsen
dc.subjectdisease mappingen
dc.subjectinformation geometryen
dc.subjectprior on correlation matricesen
dc.titlePenalising Model Component Complexity: A Principled, Practical Approach to Constructing Priorsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalStatistical Scienceen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematical Sciences, University of Bath, Bath, BA2 7AY, , United Kingdomen
dc.contributor.institutionDepartment of Mathematical Sciences, NTNU, , Norwayen
dc.contributor.institutionDepartment of Mathematics and Statistics, UiT The Arctic University of Norway, , Norwayen
kaust.authorRue, Haavarden
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