Veronica Berrocoal

Title: Identifying regions of inhomogeneities in spatial processes via an M-RA and mixture priors

Abstract: At the basis of spatial statistics is the concept of covariance function which embodies the spatial dependence in a point-referenced spatial processes. In most parametric models, the covariance function depends on few parameters among which the range parameter, which provides information about the spatial extent of the correlation, such as for example the minimum distance after which sites can be considered independent (the effective range in geostatistical terms). In most spatial analyses and models, the range of the covariance function is assumed to be a global property of the process and thus it is postulated to not vary spatially. Depending on the application, this might not be a tenable assumption.
In this talk, we present a modeling framework that allows to investigate whether a spatial process has an homogeneous spatial dependence structure and, in the case of heterogeneity in the strength of the spatial correlation, identify regions of local stationarity. To achieve this goal, we propose a modification of the Multi-Resolution Approximation (M-RA) modeling framework of Katzfuss (JASA, 2017) originally introduced as a strategy to reduce the computational burden encountered when analyzing massive spatial datasets. 
Specifically, to allow for the possibility that the correlation function of a spatial process might have a different range in different parts of a spatial domain, we provide the M-RA basis function weights with a mixture prior with one of the mixture components being a shrinking prior. We call our approach the mixture M-RA. Application of the mixture M-RA model to both stationary and non-stationary data has shown that the mixture M-RA model can handle both types of data, can correctly establish the type of spatial dependence structure in the data (e.g. stationary vs not), and can identify regions of local stationarity. In addition, assessment of the out-of-sample predictive performance of the mixture M-RA has shown that our model performs comparably to a standard stationary spatial model when the data are a realization of a stationary Gaussian process, and to a state-of-the-art non-stationary spatial model when the data are non-stationary.

 

Biography

Veronica J. Berrocal is Associate Professor of Biostatistics at the University of Michigan. Her expertise and research interests are in spatial and environmental statistics with a particular interest on development and application of statistical methods for environmental epidemiology and environmental exposure risk assessment, particularly air pollution, weather and climate modeling, and their impact on health. Dr. Berrocal is the current core co-leader of the Integrated Health Sciences Core of the University of Michigan NIEHS-funded P30 center MLEEaD – Michigan Liftetime Environmental Exposure and Disease. She has also been and is currently co-Investigator on multiple NIH-funded, HEI-funded, and NSF-funded research projects, investigating the effect of the physical and built environment on health, the impact of climate change on health, spatio-temporal modeling of traffic-related pollutants as well as studies on rheumatic diseases, and brain cancer, among others.

Prior to joining the University of Michigan as faculty, Dr. Berrocal was a postdoctoral fellow at Duke University, in the Department of Statistical Science, a postdoctoral associate at SAMSI, and a National Research Council postdoctoral research associate at the U.S. Environmental Protection Agency in the National Exposure Research Laboratory.

Veronica Berrocoal