%0 Journal Article %J ArXiv %D 2015 %T Bayesian Spatial Change of Support for Count–Valued Survey Data %A Bradley, J. R. %A Wikle, C.K. %A Holan, S. H. %X We introduce Bayesian spatial change of support methodology for count-valued survey data with known survey variances. Our proposed methodology is motivated by the American Community Survey (ACS), an ongoing survey administered by the U.S. Census Bureau that provides timely information on several key demographic variables. Specifically, the ACS produces 1-year, 3-year, and 5-year "period-estimates," and corresponding margins of errors, for published demographic and socio-economic variables recorded over predefined geographies within the United States. Despite the availability of these predefined geographies it is often of interest to data users to specify customized user-defined spatial supports. In particular, it is useful to estimate demographic variables defined on "new" spatial supports in "real-time." This problem is known as spatial change of support (COS), which is typically performed under the assumption that the data follows a Gaussian distribution. However, count-valued survey data is naturally non-Gaussian and, hence, we consider modeling these data using a Poisson distribution. Additionally, survey-data are often accompanied by estimates of error, which we incorporate into our analysis. We interpret Poisson count-valued data in small areas as an aggregation of events from a spatial point process. This approach provides us with the flexibility necessary to allow ACS users to consider a variety of spatial supports in "real-time." We demonstrate the effectiveness of our approach through a simulated example as well as through an analysis using public-use ACS data. %B ArXiv %G eng %U http://arxiv.org/abs/1405.7227 %N 1405.7227 %0 Journal Article %J ArXiv %D 2015 %T Multivariate Spatio-Temporal Models for High-Dimensional Areal Data with Application to Longitudinal Employer-Household Dynamics %A Bradley, J. R. %A Holan, S. H. %A Wikle, C.K. %X Many data sources report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate spatio-temporal dependencies. Additionally, many multivariate spatio-temporal areal datasets are extremely high-dimensional, which leads to practical issues when formulating statistical models. For example, we analyze Quarterly Workforce Indicators (QWI) published by the US Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) program. QWIs are available by different variables, regions, and time points, resulting in millions of tabulations. Despite their already expansive coverage, by adopting a fully Bayesian framework, the scope of the QWIs can be extended to provide estimates of missing values along with associated measures of uncertainty. Motivated by the LEHD, and other applications in federal statistics, we introduce the multivariate spatio-temporal mixed effects model (MSTM), which can be used to efficiently model high-dimensional multivariate spatio-temporal areal datasets. The proposed MSTM extends the notion of Moran's I basis functions to the multivariate spatio-temporal setting. This extension leads to several methodological contributions including extremely effective dimension reduction, a dynamic linear model for multivariate spatio-temporal areal processes, and the reduction of a high-dimensional parameter space using {a novel} parameter model. %B ArXiv %G eng %U http://arxiv.org/abs/1503.00982 %N 1503.00982 %0 Journal Article %J ArXiv %D 2015 %T Regionalization of Multiscale Spatial Processes using a Criterion for Spatial Aggregation Error %A Bradley, J. R. %A Wikle, C.K. %A Holan, S. H. %X The modifiable areal unit problem and the ecological fallacy are known problems that occur when modeling multiscale spatial processes. We investigate how these forms of spatial aggregation error can guide a regionalization over a spatial domain of interest. By "regionalization" we mean a specification of geographies that define the spatial support for areal data. This topic has been studied vigorously by geographers, but has been given less attention by spatial statisticians. Thus, we propose a criterion for spatial aggregation error (CAGE), which we minimize to obtain an optimal regionalization. To define CAGE we draw a connection between spatial aggregation error and a new multiscale representation of the Karhunen-Loeve (K-L) expansion. This relationship between CAGE and the multiscale K-L expansion leads to illuminating theoretical developments including: connections between spatial aggregation error, squared prediction error, spatial variance, and a novel extension of Obled-Creutin eigenfunctions. The effectiveness of our approach is demonstrated through an analysis of two datasets, one using the American Community Survey and one related to environmental ocean winds. %B ArXiv %G eng %U http://arxiv.org/abs/1502.01974 %N 1502.01974 %0 Journal Article %J ArXiv %D 2014 %T A Comparison of Spatial Predictors when Datasets Could be Very Large %A Bradley, J. R. %A Cressie, N. %A Shi, T. %K Statistics - Methodology %X

In this article, we review and compare a number of methods of spatial prediction. To demonstrate the breadth of available choices, we consider both traditional and more-recently-introduced spatial predictors. Specifically, in our exposition we review: traditional stationary kriging, smoothing splines, negative-exponential distance-weighting, Fixed Rank Kriging, modified predictive processes, a stochastic partial differential equation approach, and lattice kriging. This comparison is meant to provide a service to practitioners wishing to decide between spatial predictors. Hence, we provide technical material for the unfamiliar, which includes the definition and motivation for each (deterministic and stochastic) spatial predictor. We use a benchmark dataset of CO2 data from NASA's AIRS instrument to address computational efficiencies that include CPU time and memory usage. Furthermore, the predictive performance of each spatial predictor is assessed empirically using a hold-out subset of the AIRS data.

%B ArXiv %G eng %U http://arxiv.org/abs/1410.7748 %N 1410.7748