Improving the performance of predictive process modeling for large datasets

Finley, Andrew O.; Sang, Huiyan; Banerjee, Sudipto; Gelfand, Alan E.

doi:10.1016/j.csda.2008.09.008

Cited by 220 publications

(273 citation statements)

References 14 publications

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“…The spatial mixed effects model incorporates spatial dependence using a random linear combination of spatial basis functions. The number of terms in this linear combination is specified to be much smaller than the number of data points n, which is often called a "reduced-rank" approach to spatial prediction (Cressie and Johannesson, 2008;Banerjee et al, 2008;Finley et al, 2009;Wikle, 2010). An advantage of a reduced-rank approach is that the resulting FRK predictor can be computed very quickly.…”

Section: Spatial Predictors Under Considerationmentioning

confidence: 99%

“…To compute the FRK predictor, we used Matlab code provided by The Ohio State University's Spatial Statistics and Environmental Statistics (SSES) website (Katzfuss and Cressie, 2011b). Banerjee et al (2008) and Finley et al (2009) also use a reduced-rank approach to define a spatialpredictor called the modified predictive process (MPP). Their approach is to first predict random effects, which they call the predictive process.…”

Section: Spatial Predictors Under Considerationmentioning

confidence: 99%

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Comparing and selecting spatial predictors using local criteria

Bradley

Cressie

Shi

2014

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Remote sensing technology for the study of Earth and its environment has led to "Big Data" that, paradoxically, have global extent but may be spatially sparse. Furthermore, the variability in the measurement error and the latent process error may not fit conveniently into the Gaussian linear paradigm.In this paper, we consider the problem of selecting a predictor from a finite collection of spatial predictors of a spatial random process defined on D, a subset of d-dimensional Euclidean space. Critically, we make no statistical distributional assumptions other than additive measurement error. In this nonparametric setting, one could use a criterion based on a validation dataset to select a spatial predictor for all of D. Instead, we propose local criteria based on validation data to select a predictor at each spatial location in D; the result is a hybrid combination of the spatial predictors, which we call a locally selected predictor (LSP). We consider selection from a collection of some of the classical and more recently proposed spatial predictors currently available. In a simulation study, the relative performances of various LSPs, as well as the performance of each of the individual spatial predictors in the collection, are assessed. "Big Data" are always challenging, and here we apply LSP to a very large global spatial dataset of atmospheric CO 2 measurements.

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Section: Spatial Predictors Under Considerationmentioning

confidence: 99%

Section: Spatial Predictors Under Considerationmentioning

confidence: 99%

Comparing and selecting spatial predictors using local criteria

Bradley

Cressie

Shi

2014

TEST

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“…Banerjee et al (2010) explore these biases in greater detail. Finley et al (2009) consider modifying the predictive process by adding a heteroscedastic white-noise Gaussian process. More specifically, they propose replacingw(s) in (6) withw ǫ (s) =…”

Section: The Gaussian Predictive Processmentioning

confidence: 99%

“…More creative design of knot locations could reduce the MSPE in this case (see e.g. Finley et al, 2009). …”

Section: Synthetic Datamentioning

confidence: 99%

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Approximate Bayesian inference for large spatial datasets using predictive process models

Eidsvik¹,

Finley

Banerjee

et al. 2012

Computational Statistics & Data Analysis

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This article addresses the challenges of estimating hierarchical spatial models to large datasets. With the increasing availability of geocoded scientific data, hierarchical models involving spatial processes have become a popular method for carrying out spatial inference. This article proposes to address the computational challenges in modeling large spatial datasets by merging two recent developments. First, we use the predictive process model as a reduced-rank spatial process, to diminish the dimensionality of the model. Then we proceed to develop a computational framework for estimating predictive process models using the integrated nested Laplace approximation. We discuss settings where the first stage likelihood is Gaussian or non-Gaussian. Issues such as predictions and model comparisons are also discussed. Results are presented for synthetic data, an environmental dataset and for a large dataset on forest biomass.

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A Bayesian kriging approach for blending satellite and ground precipitation observations

Verdin

Rajagopalan

Kleiber

et al. 2015

Water Resources Research

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Drought and flood management practices require accurate estimates of precipitation. Gauge observations, however, are often sparse in regions with complicated terrain, clustered in valleys, and of poor quality. Consequently, the spatial extent of wet events is poorly represented. Satellite-derived precipitation data are an attractive alternative, though they tend to underestimate the magnitude of wet events due to their dependency on retrieval algorithms and the indirect relationship between satellite infrared observations and precipitation intensities. Here we offer a Bayesian kriging approach for blending precipitation gauge data and the Climate Hazards Group Infrared Precipitation satellite-derived precipitation estimates for Central America, Colombia, and Venezuela. First, the gauge observations are modeled as a linear function of satellite-derived estimates and any number of other variables-for this research we include elevation. Prior distributions are defined for all model parameters and the posterior distributions are obtained simultaneously via Markov chain Monte Carlo sampling. The posterior distributions of these parameters are required for spatial estimation, and thus are obtained prior to implementing the spatial kriging model. This functional framework is applied to model parameters obtained by sampling from the posterior distributions, and the residuals of the linear model are subject to a spatial kriging model. Consequently, the posterior distributions and uncertainties of the blended precipitation estimates are obtained. We demonstrate this method by applying it to pentadal and monthly total precipitation fields during 2009. The model's performance and its inherent ability to capture wet events are investigated. We show that this blending method significantly improves upon the satellite-derived estimates and is also competitive in its ability to represent wet events. This procedure also provides a means to estimate a full conditional distribution of the ''true'' observed precipitation value at each grid cell.

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Improving the performance of predictive process modeling for large datasets

Cited by 220 publications

References 14 publications

Comparing and selecting spatial predictors using local criteria

Comparing and selecting spatial predictors using local criteria

Approximate Bayesian inference for large spatial datasets using predictive process models

A Bayesian kriging approach for blending satellite and ground precipitation observations

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