Objective Bayesian Analysis of Spatially Correlated Data

Berger, James O.; Oliveira, Victor De; Sansó, Bruno

doi:10.1198/016214501753382282

Cited by 404 publications

(401 citation statements)

References 22 publications

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“…and t(x) i = c(x, x i ) and P (x) = h(x) T − t(x) T A −1 H. We follow the suggestion of Berger et al (2001) and assume a vague prior (β, σ 2 ) that is proportional to σ 2 , an approach that has been adopted by several other studies, including Oakley and O'Hagan (2002), Bastos andO'Hagan (2009), Araya-Melo et al (2015), and . The posterior distribution of the GCM output is a Student's t distribution with n − q degrees of freedom, but is sufficiently close to being Gaussian for this application.…”

Section: Theoretical Basis Of the Emulatormentioning

confidence: 99%

Emulation of long-term changes in global climate: application to the late Pliocene and future

et al. 2017

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Abstract. Multi-millennial transient simulations of climate changes have a range of important applications, such as for investigating key geologic events and transitions for which high-resolution palaeoenvironmental proxy data are available, or for projecting the long-term impacts of future climate evolution on the performance of geological repositories for the disposal of radioactive wastes. However, due to the high computational requirements of current fully coupled general circulation models (GCMs), long-term simulations can generally only be performed with less complex models and/or at lower spatial resolution. In this study, we present novel longterm "continuous" projections of climate evolution based on the output from GCMs, via the use of a statistical emulator. The emulator is calibrated using ensembles of GCM simulations, which have varying orbital configurations and atmospheric CO 2 concentrations and enables a variety of investigations of long-term climate change to be conducted, which would not be possible with other modelling techniques on the same temporal and spatial scales. To illustrate the potential applications, we apply the emulator to the late Pliocene (by modelling surface air temperature -SAT), comparing its results with palaeo-proxy data for a number of global sites, and to the next 200 kyr (thousand years) (by modelling SAT and precipitation). A range of CO 2 scenarios are prescribed for each period. During the late Pliocene, we find that emulated SAT varies on an approximately precessional timescale, with evidence of increased obliquity response at times. A comparison of atmospheric CO 2 concentration for this period, estimated using the proxy sea surface temperature (SST) data from different sites and emulator results, finds that relatively similar CO 2 concentrations are estimated based on sites at lower latitudes, whereas higher-latitude sites show larger discrepancies. In our second illustrative application, spanning the next 200 kyr into the future, we find that SAT oscillations appear to be primarily influenced by obliquity for the first ∼ 120 kyr, whilst eccentricity is relatively low, after which precession plays a more dominant role. Conversely, variations in precipitation over the entire period demonstrate a strong precessional signal. Overall, we find that the emulator provides a useful and powerful tool for rapidly simulating the long-term evolution of climate, both past and future, due to its relatively high spatial resolution and relatively low computational cost. However, there are uncertainties associated with the approach used, including the inability of the emulaPublished by Copernicus Publications on behalf of the European Geosciences Union. 1540 N. S. Lord et al.: Emulation of long-term changes in global climate tor to capture deviations from a quasi-stationary response to the forcing, such as transient adjustments of the deep-ocean temperature and circulation, in addition to its limited range of fixed ice sheet configurations and its requirement for prescribed atmos...

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Section: Theoretical Basis Of the Emulatormentioning

confidence: 99%

Emulation of long-term changes in global climate: application to the late Pliocene and future

et al. 2017

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“…The likelihood function is numerically optimized for φ, and τ 2 rel , because no analytical expression exists for these two parameters. Bayesian inference treats the parameters as unknown stochastic variables and, as such, incorporates the uncertainty of all parameters (Gelman et al 2003;Berger et al 2001). Bayesian inference it attractive in the case of sparse data, since additional prior information can be used, thereby improving the estimation accuracy (see, for example, Cui et al 1995).…”

Section: Restricted Maximum Likelihood Versus Bayesian Inferencementioning

confidence: 99%

External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

et al. 2007

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In the mid nineteen eighties the Dutch NO x air quality monitoring network was reduced from 73 to 32 rural and city background stations, leading to higher spatial uncertainties. In this study, several other sources of information are being used to help reduce uncertainties in parameter estimation and spatial mapping. For parameter estimation, we used Bayesian inference. For mapping, we used kriging with external drift (KED) including secondary information from a dispersion model. The methods were applied to atmospheric NO x concentrations on rural and urban scales. We compared Bayesian estimation with restricted maximum likelihood estimation and KED with universal kriging. As a reference we also included ordinary least squares (OLS). Comparison of several parameter estimation and spatial interpolation methods was done by cross-validation. Bayesian analysis resulted in an error reduction of 10 to 20% as compared to restricted maximum likelihood, whereas KED resulted in an error reduction of 50% as compared to universal kriging. Where observations were sparse, the predictions were substantially improved by inclusion of the dispersion model output and by using available prior information. No major improvement was observed as compared to OLS, the cause presumably being that much good information is contained in the dispersion model output, so that no additional spatial residual random field is required to explain the data. In all, we conclude that reduction in the monitoring network could be compensated by modern geostatistical methods, and that a traditional simple statistical model is of an almost equal quality.

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“…It the spatial and computer experiments literatures it has become convention to deploy a reference π(τ 2 ) ∝ 1/τ 2 prior (Berger, De Oliveira, and Sanso 2001) and obtain a marginal likelihood for the remaining unknowns: …”

Section: Inference and Predictionmentioning

confidence: 99%

laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes inR

Gramacy¹

2016

J. Stat. Soft.

157

142

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Gaussian process (GP) regression models make for powerful predictors in out of sample exercises, but cubic runtimes for dense matrix decompositions severely limit the size of data -training and testing -on which they can be deployed. That means that in computer experiment, spatial/geo-physical, and machine learning contexts, GPs no longer enjoy privileged status as data sets continue to balloon in size. We discuss an implementation of local approximate Gaussian process models, in the laGP package for R, that offers a particular sparse-matrix remedy uniquely positioned to leverage modern parallel computing architectures. The laGP approach can be seen as an update on the spatial statistical method of local kriging neighborhoods. We briefly review the method, and provide extensive illustrations of the features in the package through worked-code examples. The appendix covers custom building options for symmetric multi-processor and graphical processing units, and built-in wrapper routines that automate distribution over a simple network of workstations.

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Objective Bayesian Analysis of Spatially Correlated Data

Cited by 404 publications

References 22 publications

Emulation of long-term changes in global climate: application to the late Pliocene and future

Emulation of long-term changes in global climate: application to the late Pliocene and future

External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

laGP: Large-Scale Spatial Modeling via Local Approximate Gaussian Processes inR

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