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

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    euclid.ss.1491465621.pdf
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    Type
    Article
    Authors
    Simpson, Daniel
    Rue, Haavard cc
    Riebler, Andrea
    Martins, Thiago G.
    Sørbye, Sigrunn H.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Statistics Program
    Date
    2017-04-06
    Online Publication Date
    2017-04-06
    Print Publication Date
    2017-02
    Permanent link to this record
    http://hdl.handle.net/10754/623413
    
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    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.
    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.
    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.
    Publisher
    Institute of Mathematical Statistics
    Journal
    Statistical Science
    DOI
    10.1214/16-STS576
    arXiv
    1403.4630
    Additional Links
    http://projecteuclid.org/euclid.ss/1491465621
    ae974a485f413a2113503eed53cd6c53
    10.1214/16-STS576
    Scopus Count
    Collections
    Articles; Statistics Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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