Seminari d'Estadística i Investigació Operativa amb Haavard Rue (King Abdullah University)

SEMINARI D'ESTADISTICA I INVESTIGACIO OPERATIVA, UPC.
 
DATA: Dimecres 22 de març de 2017, Hora: 14:00
PONENT: Haavard Rue, King Abdullah University of Science and Technology, Saudi Arabia

LLOC: FME, Edifici U, Sala de juntes
      Campus Sud, UPC, Pau Gargallo, 5, 02028 Barcelona

TITOL: Penalising model component complexity: A principled practical approach to constructing priors

RESUM: Setting prior distributions on model parameters is the act of characterising the nature of our uncertainty and has proven a critical issue in applied Bayesian statistics. Although the prior distribution should ideally encode the users' uncertainty about the parameters, this level of knowledge transfer seems to be unattainable in practice and applied statisticians are forced to search for a "default" prior. Despite the development of objective priors, which are only available explicitly for a small number of highly restricted model classes, the applied statistician has few practical guidelines to follow when choosing the priors. An easy way out of this dilemma is to re-use prior choices of others, with an appropriate reference.

In this talk, I will 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, like random effect models, spline smoothing, disease mapping, Cox proportional hazard models with time-varying frailty, spatial Gaussian fields and multivariate probit models. Further, we show how to control the overall variance arising from many model components in hierarchical models. This is onging work within the www.r-inla.org project, with Daniel Simpson (Bath), Andrea Riebler, Geir-Arne Fuglstad (NTNU) and Sigrunn Sorbye (Univ. of Tromso) and others.

SOBRE L'AUTOR:

Haavard Rue is currently Professor at the Division for Computer, Electrical and Mathematical Science and Engineering of the King Abdullah University of Science and Technology in Saudi Arabia, and has been Professor at the Department of Mathematical Sciences of the Norwegian University of Science and Technology (NTNU) in Trondheim, Norway, for many years. He has given 15 invited plenum and keynote talks at larger conferences. He has directed 25 PhD students, and served as associate editor for several journals, among others the Journal of the Royal Statistical Society, Series B, Scandinavian Journal of Statistics and the Annals of of Statistics. He is principal investigator of several large Norwegian research projects, and has taught over 25 courses and lectures on "Bayesian computing with INLA" around the world, and has (co-)authored well over 150 research articles in scientific journals. His main research interests are Computational Bayesian statistics, Bayesian methodology for priors, sensitivity and robustness, Integrated Nested Laplace Approximations (INLA), Gaussian Markov random fields, Models for dependent data, Stochastic partial differential equations for spatial modeling and Bayesian statistical models for extreme data scales. For more information on his research see his personal web page https://www.kaust.edu.sa/en/study/faculty/haavard-rue