Spatial statistics and Gaussian processes: A beautiful marriage

Gelfand, Alan E.; Schliep, Erin M.

doi:10.1016/j.spasta.2016.03.006

Cited by 116 publications

(79 citation statements)

References 37 publications

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“…Gaussian processes (GPs) are popular geostatistical modeling tools due to their flexibility and ability to quantify uncertainty in nonparametric regressions (Neal, 1998;O'Hagan, 1978). Good GP modeling overviews are provided in Cressie (1993), Rasmussen and Williams (2006), Cressie andWikle (2011), andSchliep (2016). Banerjee, Carlin, and Gelfand (2015) discussed Bayesian aspects of GPs.…”

Section: Introductionmentioning

confidence: 99%

A large‐scale spatio‐temporal binomial regression model for estimating seroprevalence trends

et al. 2018

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This paper develops a large‐scale Bayesian spatio‐temporal binomial regression model to investigate regional trends in antibody prevalence to Borrelia burgdorferi, the causative agent of Lyme disease. Our model uses Gaussian predictive processes to estimate the spatially varying trends and a conditional autoregressive scheme to account for spatio‐temporal dependence. A novel framework, easily scalable to large spatio‐temporal data, is developed. The proposed model is used to analyze about 16 million B. burgdorferi antibody Lyme tests performed on canine samples in the conterminous United States over the sixty‐month period from January 2012 to December 2016. This analysis identifies areas of increasing canine Lyme disease risk; prevalence of infection is getting worse in endemic regions and increases are also seen in non‐endemic regions. Because Lyme disease is zoonotic, affecting both humans and dogs, the analysis also serves to pinpoint areas of increasing human risk.

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Section: Introductionmentioning

confidence: 99%

A large‐scale spatio‐temporal binomial regression model for estimating seroprevalence trends

et al. 2018

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“…While this assumption is difficult to check, it follows from assuming that the RF is weakly stationary and Gaussian (4). The assumption of Gaussian data lies at the heart of many spatial analyses (Gelfand and Schliep 2016) and is easily checked with a QQ plot. The assumption of weak stationarity may be questionable for spatial data over large geographic regions and methods have been developed for testing this assumption (see, e.g., Corstanje, Grunwald, and Lark 2008;Fuentes 2005;Jun and Genton 2012;Bandyopadhyay and Subba Rao 2017).…”

Section: Discussionmentioning

confidence: 99%

spTest: An R Package Implementing Nonparametric Tests of Isotropy

Weller¹

2018

J. Stat. Soft.

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An important step in modeling spatially-referenced data is appropriately specifying the second order properties of the random field. A scientist developing a model for spatial data has a number of options regarding the nature of the dependence between observations. One of these options is deciding whether or not the dependence between observations depends on direction, or, in other words, whether or not the spatial covariance function is isotropic. Isotropy implies that spatial dependence is a function of only the distance and not the direction of the spatial separation between sampling locations. A researcher may use graphical techniques, such as directional sample semivariograms, to determine whether an assumption of isotropy holds. These graphical diagnostics can be difficult to assess, subject to personal interpretation, and potentially misleading as they typically do not include a measure of uncertainty. In order to escape these issues, a hypothesis test of the assumption of isotropy may be more desirable. To avoid specification of the covariance function, a number of nonparametric tests of isotropy have been developed using both the spatial and spectral representations of random fields. Several of these nonparametric tests are implemented in the R package spTest, available on CRAN. We demonstrate how graphical techniques and the hypothesis tests programmed in package spTest can be used in practice to assess isotropy properties.

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“…As a first demonstration of the PP-RB method, we apply it to fit the standard geostatistical model (Cressie, 1990), which is very commonly used in environmental and Parametric geostatistical modeling involves the use of Gaussian processes that are ubiquitous throughout many different fields and are readily extended to the temporal and spatio-temporal contexts (Cressie and Wikle, 2011) as well as commonly employed in computer model emulation (e.g., Higdon et al, 2008) and trajectory estimation (e.g., Hooten and Johnson, 2017). The use of Gaussian processes in spatially-explicit models has a long history in statistics, but has experienced a resurgence lately due to the need to flexibly and efficiently model large data sets and provide optimal predictions in space and time (Gelfand and Schliep, 2016;Heaton et al, 2019).…”

Section: Pp-rb Application To Geostatisticsmentioning

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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Spatial statistics and Gaussian processes: A beautiful marriage

Cited by 116 publications

References 37 publications

A large‐scale spatio‐temporal binomial regression model for estimating seroprevalence trends

A large‐scale spatio‐temporal binomial regression model for estimating seroprevalence trends

spTest: An R Package Implementing Nonparametric Tests of Isotropy

Making Recursive Bayesian Inference Accessible

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