Spatial subsemble estimator for large geostatistical data

Barbian, Márcia Helena; Assunção, Renato M.

doi:10.1016/j.spasta.2017.08.004

Cited by 25 publications

(17 citation statements)

References 26 publications

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“…Further, the assumption of independence across subregions allows the likelihood for β, θ and φ d is to be computed in parallel thereby facilitating computation. By way of distinction, this approach is inherently different from the "divide and conquer" approach (Liang et al, 2013;Barbian and Assunção, 2017). In the divide and conquer approach, the full dataset is subsampled, the model is fit to each subset and the results across subsamples are pooled.…”

Section: Spatial Partitioningmentioning

confidence: 99%

“…For example, Paciorek et al (2015) show how (1.1) can be calculated using parallel computing while Katzfuss and Hammerling (2017) and Katzfuss (2017) develop a basisfunction approach that lends itself to distributed computing. Alternatively, Barbian and Assunc ¸ão (2017) and Guhaniyogi and Banerjee (2018) propose dividing the data into a large number of subsets, draw inference on the subsets in parallel and then combining the inferences. Datta et al (2016a,b) build upon Vecchia (1988) by developing novel approaches to factoring (1.1) as a series of conditional distributions based only on nearest neighbors.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Case Study Competition Among Methods for Analyzing Large Spatial Data

Heaton

Datta

Finley

et al. 2018

JABES

337

277

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The Gaussian process is an indispensable tool for spatial data analysts. The onset of the “big data” era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various alternatives to the full Gaussian process that are more amenable to handling big spatial data have been proposed. These modern methods often exploit low-rank structures and/or multi-core and multi-threaded computing environments to facilitate computation. This study provides, first, an introductory overview of several methods for analyzing large spatial data. Second, this study describes the results of a predictive competition among the described methods as implemented by different groups with strong expertise in the methodology. Specifically, each research group was provided with two training datasets (one simulated and one observed) along with a set of prediction locations. Each group then wrote their own implementation of their method to produce predictions at the given location and each was subsequently run on a common computing environment. The methods were then compared in terms of various predictive diagnostics. Supplementary materials regarding implementation details of the methods and code are available for this article online. Electronic Supplementary Material Supplementary materials for this article are available at 10.1007/s13253-018-00348-w.

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Section: Spatial Partitioningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Case Study Competition Among Methods for Analyzing Large Spatial Data

Heaton

Datta

Finley

et al. 2018

JABES

337

277

View full text Add to dashboard Cite

show abstract

“…Furthermore, any of the alternative approaches for approximating Gaussian process covariance matrices using reduced-rank or sparse parameterizations (e.g., Higdon, 2002;Furrer et al, 2006;Cressie and Johannesson, 2008;Lindgren et al, 2011;Gramacy et al, 2015;Nychka et al, 2015;Katzfuss, 2017) are also compatible with our PP-RB method, as long as they are applied in a Bayesian context (also see Heaton et al, ods (e.g., Liang et al, 2013;Kleiner et al, 2014;MacLaurin and Adams, 2015;Barbian and Assuncao, 2017) with PP-RB to reduce computational requirements further.…”

Section: Discussionmentioning

confidence: 99%

Making Recursive Bayesian Inference Accessible

Hooten

Johnson

Brost

2019

The American Statistician

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Bayesian models provide recursive inference naturally because they can formally reconcile new data and existing scientific information. However, popular use of Bayesian methods often avoids priors that are based on exact posterior distributions resulting from former studies. Two existing Recursive Bayesian methods are: Prior-and Proposal-Recursive Bayes. Prior-Recursive Bayes uses Bayesian updating, fitting models to partitions of data sequentially, and provides a way to accommodate new data as they become available using the posterior from the previous stage as the prior in the new stage based on the latest data. Proposal-Recursive Bayes is intended for use with hierarchical Bayesian models and uses a set of transient priors in first stage independent analyses of the data partitions. The second stage of Proposal-Recursive Bayes uses the posteriors from the first stage as proposals in an MCMC algorithm to fit the full model. We combine Prior-and Proposal-Recursive concepts to fit any Bayesian model, and often with computational improvements. We demonstrate our method with two case studies. Our approach has implications for big data, streaming data, and optimal adaptive design situations.

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“…Over the last few decades the spatial statistics community has attacked this big GP problem from many fronts and offered many different and efficient solutions to ease the computational burden. Methods include sparse nearest neighbor approximations (Vecchia, 1988;Stein et al, 2004;Datta et al, 2016a), low-rank approximations (Banerjee et al, 2008;Cressie and Johannesson, 2008), sparse-plus-low-rank method (Ma et al, 2019), multi-resolutional approach (Katzfuss, 2017), data partitioning (Barbian and Assunção, 2017;Guhaniyogi and Banerjee, 2018), covariance tapering (Furrer et al, 2006;Kaufman et al, 2008), stochastic partial differential equations (Lindgren et al, 2011), composite likelihoods (Bevilacqua and Gaetan, 2015;Eidsvik et al, 2014), gridbased methods (Nychka et al, 2015;Guinness and Fuentes, 2017;Stroud et al, 2017), among others. A comprehensive review of all these methods is beyond the scope of this paper but we refer the readers to the articles Sun et al (2012); Bradley et al (2016); Banerjee (2017); Heaton et al (2019); Banerjee (2020) for reviews and comparisons of the methods.…”

Section: Introductionmentioning

confidence: 99%

Sparse nearest neighbor Cholesky matrices in spatial statistics

Datta¹

2021

Preprint

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Gaussian Processes (GP) is a staple in the toolkit of a spatial statistician. Well-documented computing roadblocks in the analysis of large geospatial datasets using Gaussian Processes have now largely been mitigated via several recent statistical innovations. Nearest Neighbor Gaussian Processes (NNGP) has emerged as one of the leading candidate for such massive-scale geospatial analysis owing to their empirical success. This articles reviews the connection of NNGP to sparse Cholesky factors of the spatial precision (inverse-covariance) matrix. Focus of the review is on these sparse Cholesky matrices which are versatile and have recently found many diverse applications beyond the primary usage of NNGP for fast parameter estimation and prediction in the spatial (generalized) linear models. In particular, we discuss applications of sparse NNGP Cholesky matrices to address multifaceted computational issues in spatial bootstrapping, simulation of large-scale realizations of Gaussian random fields, and extensions to non-parametric mean function estimation of a Gaussian Process using Random Forests. We also review a sparse-Cholesky-based model for areal (geographically-aggregated) data that addresses long-established interpretability issues of existing areal models. Finally, we highlight some yet-to-be-addressed issues of such sparse Cholesky approximations that warrants further research.

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Spatial subsemble estimator for large geostatistical data

Cited by 25 publications

References 26 publications

A Case Study Competition Among Methods for Analyzing Large Spatial Data

A Case Study Competition Among Methods for Analyzing Large Spatial Data

Making Recursive Bayesian Inference Accessible

Sparse nearest neighbor Cholesky matrices in spatial statistics

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