Hierarchical Modeling and Analysis for Spatial Data

Banerjee, Sudipto; Carlin, Bradley P.; Gelfand, Alan E.

doi:10.1201/b17115

Cited by 1,412 publications

(1,509 citation statements)

References 0 publications

Supporting

Mentioning

1,486

Contrasting

Unclassified

Order By: Relevance

“…Moreover, spatial units with a similar environmental composition will often be characterized by similar abundances. Explicitly accounting for these patterns in the estimation process could lead to increased accuracy in estimation, possibly by modeling the relative abundances N ij as a function of environmental variables or as a function of spatial effects (e.g., using conditional autoregression effects in a hierarchical model; Banerjee et al, 2004). Alternatively, it would be possible to maximize a regularized log-likelihood, such as…”

Section: Limitations and Extensionsmentioning

confidence: 99%

Capitalizing on Opportunistic Data for Monitoring Relative Abundances of Species

et al. 2015

View full text Add to dashboard Cite

With the internet, a massive amount of information on species abundance can be collected by citizen science programs. However, these data are often difficult to use directly in statistical inference, as their collection is generally opportunistic, and the distribution of the sampling effort is often not known. In this article, we develop a general statistical framework to combine such "opportunistic data" with data collected using schemes characterized by a known sampling effort. Under some structural assumptions regarding the sampling effort and detectability, our approach makes it possible to estimate the relative abundance of several species in different sites. It can be implemented through a simple generalized linear model. We illustrate the framework with typical bird datasets from the Aquitaine region in south-western France. We show that, under some assumptions, our approach provides estimates that are more precise than the ones obtained from the dataset with a known sampling effort alone. When the opportunistic data are abundant, the gain in precision may be considerable, especially for rare species. We also show that estimates can be obtained even for species recorded only in the opportunistic scheme. Opportunistic data combined with a relatively small amount of data collected with a known effort may thus provide access to accurate and precise estimates of quantitative changes in relative abundance over space and/or time.

show abstract

Section: Limitations and Extensionsmentioning

confidence: 99%

Capitalizing on Opportunistic Data for Monitoring Relative Abundances of Species

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Note that the common spatial variance parameter does not affect (7) because it cancels in the product CS 1 w . Also, there is no contribution from the means of either Á lt or w lt in (7) since these have been assumed to be 0.…”

Section: Autoregressive Models With Gaussian Predictive Process Appromentioning

confidence: 99%

“…where Q Á lt is as given in (7). Analogous to (5), we specify w lt at the knots conditionally, given w lt 1 , by…”

Section: Autoregressive Models With Gaussian Predictive Process Appromentioning

confidence: 99%

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Sahu

Bakar

2012

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases temporal data are obtained by registering events, for example telecommunication or web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time auto-regressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method (Banerjee et al. [1]) is extended to include auto-regressive terms of latent space-time processes. Specifically, a spacetime auto-regressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-hour average ground level ozone concentration data from 1997 to 2006 from a large study region in the eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of non-compliance with respect to the standard, are obtained and illustrated.

show abstract

“…To overcome both the spatial smoothing and the voxelwise analysis critiques, a limited number of spatial models have been proposed for neuroimaging data (e.g., Besag, 1986;Hartvig and Jensen, 2000;Banerjee, Carlin, and Gelfand, 2004;Bowman et al, 2008;Shi et al, 2011). Development and implementation of these more sophisticated models has been slow in coming not only because deciphering the structure of spatial dependence in brain images can be difficult but also because spatial models are complex, which often translates into the nontrivial concern of high computation costs (Lazar, 2008).…”

Section: Spatial Modeling Of Neuroimaging Datamentioning

confidence: 99%

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time‐Varying Covariates

2012

View full text Add to dashboard Cite

Summary Neuroimaging data collected at repeated occasions are gaining increasing attention in the neuroimaging community due to their potential in answering questions regarding brain development, aging, and neurodegeneration. These datasets are large and complicated, characterized by the intricate spatial dependence structure of each response image, multiple response images per subject, and covariates that may vary with time. We propose a multiscale adaptive generalized method of moments (MA-GMM) approach to estimate marginal regression models for imaging datasets that contain time-varying, spatially-related responses and some time-varying covariates. Our method categorizes covariates into types to determine the valid moment conditions to combine during estimation. Further, instead of assuming independence of voxels (the components that make up each subject’s response image at each time point) as many current neuroimaging analysis techniques do, this method “adaptively smoothes” neuroimaging response data, computing parameter estimates by iteratively building spheres around each voxel and combining observations within the spheres with weights. MA-GMM’s development adds to the few available modeling approaches intended for longitudinal imaging data analysis. Simulation studies and an analysis of a real longitudinal imaging dataset from the Alzheimer’s Disease Neuroimaging Initiative are used to assess the performance of MA-GMM.

show abstract

Hierarchical Modeling and Analysis for Spatial Data

Cited by 1,412 publications

References 0 publications

Capitalizing on Opportunistic Data for Monitoring Relative Abundances of Species

Capitalizing on Opportunistic Data for Monitoring Relative Abundances of Species

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Multiscale Adaptive Marginal Analysis of Longitudinal Neuroimaging Data with Time‐Varying Covariates

Contact Info

Product

Resources

About