Prof.ssa Veronica Berrocal
University of Department of Biostatistics, University of Michigan
Abstract
In this talk, we present two methods to adaptively smooth spatial areal/lattice datasets. Both statistical models extend the seminal conditionally autoregressive model (CAR) of Besag (1974). In the first part of the talk, we consider a pre-surgical brain analysis application and propose a novel spatially adaptive conditionally smoothing model that allows to smooth functional magnetic resonance imaging (fMRI) data without blurring any sharp boundaries between activated and deactivated regions, ensuring spatial accuracy. Our spatially adaptive conditionally autoregressive model, that we call CWAS, has variances in the full conditionals of the means that are proportional to error variances, allowing the degree of smoothing to vary across the brain. In the second part of the talk, we present another extension of the binary adjacency proximities conditionally autoregressive (CAR) model (Besag 1974) where the proximities, defined through a suitable transformation of a latent Gaussian process are random and directional, thus allowing for varying strength of association among an areal unit and its neighbors. Our specification of the proximities allows us to derive distributional properties of the proximities and of the spatial random effects, and leads to tractable Bayesian inference with closed form full conditionals. We illustrate the capabilities of this model with an application to car accident data for the state of Michigan in years 1990-2004.
Organizzatore
Prof.ssa Daniela Cocchi