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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.