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Statistics Colloquium
December 2 (Fri) 11 a.m.
Alavi Commons Room, 6625 Everett Tower

Adaptive directional spatial smoothing for epidemiological data

Veronica Berrocal, Ph.D.
Associate Professor of Biostatistics
University of Michigan

Abstract:
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.

Bio:
Veronica J. Berrocal is an Associate Professor of Biostatistics in the University of Michigan School of Public Health. She received her Ph.D. in Statistics from the University of Washington in 2007. Following her graduation, Veronica was a National Research Council Postdoctoral Associate at the US Environmental Protection Agency. In 2009, she was a Postdoctoral fellow at the Department of Statistical Sciences at Duke University. In 2010, she was a Postdoctoral Associate at the Statistical and Applied Mathematical Sciences Institute (SAMSI).

Veronica's research focuses on developing and applying statistical models for data collected over space and/or over time. Her main applications are related to atmospheric sciences (weather and climate data), environmental/social epidemiology (exposure to pollutants, heat, weather, built-environment, etc.), rheumatology, and also some image data.

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All statistics graduate students are expected to attend.

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