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Title: On multivariate CAR models for multivariate disease mapping: The state of the art Authors:  Ying C MacNab - University of British Columbia (Canada) [presenting]
Abstract: Multivariate disease mapping has been a very active area of research in recent decade. Notable progresses have been made in the formulation of flexible proper multivariate conditional autoregressive (MpCAR) models. One attractive feature of this class of MpCARs is that they can be formulated to model multivariate spatial dependencies, including (a)symmetric cross-dependencies and (a)symmetric cross-covariance functions. These MpCARs are typically used as disease risks priors within a Bayesian hierarchical inferential framework, to enable multivariate spatial smoothing and posterior risk prediction and inference. A brief survey of the recent proposals of MpCARs will be given, with a focus on enforcement for positive definiteness via constrained parameterization or reparameterization. Sufficient as well as sufficient and necessary constraints and related computational options are presented. They are the current state-of-the-art and are of central importance in posterior estimation and inference of Bayesian hierarchical models using MpCARs.