An integrated Bayesian model for estimating the long-term health effects of air pollution by fusing modelled and measured pollution data: a case study of nitrogen dioxide concentrations in Scotland

The long-term health effects of air pollution can be estimated using a spatio-temporal ecological study, where the disease data are counts of hospital admissions from populations in small areal units at yearly intervals. Spatially representative pollution concentrations for each areal unit are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over grid level concentrations from an atmospheric dispersion model. We propose a novel fusion model for estimating spatially aggregated pollution concentrations using both the modelled and monitored data, and relate these concentrations to respiratory disease in a new study in Scotland between 2007 and 2011

Bayesian Semiparametric Hierarchical Empirical Likelihood Spatial Models

We introduce a general hierarchical Bayesian framework that incorporates a flexible nonparametric data model specification through the use of empirical likelihood methodology, which we term semiparametric hierarchical empirical likelihood (SHEL) models. Although general dependence structures can be readily accommodated, we focus on spatial modeling, a relatively underdeveloped area in the empirical likelihood literature. Importantly, the models we develop naturally accommodate spatial association on irregular lattices and irregularly spaced point-referenced data. We illustrate our proposed framework by means of a simulation study and through three real data examples. First, we develop a spatial Fay-Herriot model in the SHEL framework and apply it to the problem of small area estimation in the American Community Survey. Next, we illustrate the SHEL model in the context of areal data (on an irregular lattice) through the North Carolina sudden infant death syndrome (SIDS) dataset. Finally, we analyze a point-referenced dataset from the North American Breeding Bird survey that considers dove counts for the state of Missouri. In all cases, we demonstrate superior performance of our model, in terms of mean squared prediction error, over standard parametric analyses.Comment: 29 pages, 3 figue

Estimating Abundance from Counts in Large Data Sets of Irregularly-Spaced Plots using Spatial Basis Functions

Monitoring plant and animal populations is an important goal for both academic research and management of natural resources. Successful management of populations often depends on obtaining estimates of their mean or total over a region. The basic problem considered in this paper is the estimation of a total from a sample of plots containing count data, but the plot placements are spatially irregular and non randomized. Our application had counts from thousands of irregularly-spaced aerial photo images. We used change-of-support methods to model counts in images as a realization of an inhomogeneous Poisson process that used spatial basis functions to model the spatial intensity surface. The method was very fast and took only a few seconds for thousands of images. The fitted intensity surface was integrated to provide an estimate from all unsampled areas, which is added to the observed counts. The proposed method also provides a finite area correction factor to variance estimation. The intensity surface from an inhomogeneous Poisson process tends to be too smooth for locally clustered points, typical of animal distributions, so we introduce several new overdispersion estimators due to poor performance of the classic one. We used simulated data to examine estimation bias and to investigate several variance estimators with overdispersion. A real example is given of harbor seal counts from aerial surveys in an Alaskan glacial fjord.Comment: 37 pages, 7 figures, 4 tables, keywords: sampling, change-of-support, spatial point processes, intensity function, random effects, Poisson process, overdispersio

Bayesian Modeling of Incompatible Spatial Data: A Case Study Involving Post-Adrian Storm Forest Damage Assessment

Incompatible spatial data modeling is a pervasive challenge in remote sensing data analysis that involves field data. Typical approaches to addressing this challenge aggregate information to a coarser common scale, i.e., compatible resolutions. Such pre-processing aggregation to a common resolution simplifies analysis, but potentially causes information loss and hence compromised inference and predictive performance. To incorporate finer information to enhance prediction performance, we develop a new Bayesian method aimed at improving predictive accuracy and uncertainty quantification. The main contribution of this work is an efficient algorithm that enables full Bayesian inference using finer resolution data while optimizing computational and storage costs. The algorithm is developed and applied to a forest damage assessment for the 2018 Adrian storm in Carinthia, Austria, which uses field data and high-resolution LiDAR measurements. Simulation studies demonstrate that this approach substantially improves prediction accuracy and stability, providing more reliable inference to support forest management decisions.Comment: 15 pages, 10 figure