Estimation and Model Identification for Continuous Spatial Processes

Vecchia, Aldo V.

doi:10.1111/j.2517-6161.1988.tb01729.x

Cited by 366 publications

(416 citation statements)

References 13 publications

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“…This approach requires the inversion of a very large variancecovariance matrix to evaluate the joint distribution of the random field, on operation that is not practical for witness tree data that may involve tens or even hundreds of thousands of surveyed trees. Approximate likelihood methods of Vecchia (1988) were considered, but the resulting Markov Chain Monte Carlo algorithm yielded a chain with very strong autocorrelations among iterates, and failed to converge within even 50,000 iterations.…”

Section: Data Modelmentioning

confidence: 99%

Modeling and spatial prediction of pre-settlement patterns of forest distribution using witness tree data

Rathbun

Black

2006

Environ Ecol Stat

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At the time of European settlement, land surveys were conducted progressively westward throughout the United States. Outside of the original 13 colonies, surveys generally followed the Public Land Survey system in which trees, called witness trees, were regularly recorded at 1 mi by 1 mi grid intersections. This unintentional sampling provides insight into the composition and structure of pre-European settlement forests, which is used as baseline data to assess forest change following settlement. In this paper, a model for the Public Land Surveys of east central Alabama is developed. Assuming that the locations of trees of each species are realized from independent Poisson processes whose respective log intensities are linear functions of environmental covariates (i.e., elevation, landform, and physiographic province), the species observed at the survey grid intersections are independently sampled from a generalized logistic regression model. If all 68 species found in the survey were included, the model would be highly over-parameterized, so only the distribution of the most common taxon, pines, will be considered at this time. To assess the impact of environmental factors not included in the model, a hidden Gaussian random field shall be added as a random effect. A Markov Chain Monte Carlo algorithm is developed for Bayesian inference on model parameters, and for Bayes posterior prediction of the spatial distribution of pines in east central Alabama.

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Section: Data Modelmentioning

confidence: 99%

Modeling and spatial prediction of pre-settlement patterns of forest distribution using witness tree data

Rathbun

Black

2006

Environ Ecol Stat

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“…When φ 1 = 0.5, (7) reduces to the exponential covariance function exp (− |s/φ 2 |), which is identical to (8) with φ 1 = 1, while as φ 1 → ∞, (7) converges to exp  − (s/φ 2 ) 2 /2  , but non-nested tests can choose between (7) and (8). A number of other models, and their fitting to irregularlyspaced data, have been considered by, e.g., Vecchia (1988), Jones and Vecchia (1993), Handcock and Wallis (1994), Stein et al (2004) and Fuentes (2007).…”

Section: Spatial Correlation Modelsmentioning

confidence: 99%

Non-nested testing of spatial correlation

Delgado

Robinson

2015

Journal of Econometrics

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a b s t r a c tWe develop non-nested tests in a general spatial, spatio-temporal or panel data context. The spatial aspect can be interpreted quite generally, in either a geographical sense, or employing notions of economic distance, or when parametric modelling arises in part from a common factor or other structure. In the former case, observations may be regularly-spaced across one or more dimensions, as is typical with much spatio-temporal data, or irregularly-spaced across all dimensions; both isotropic models and nonisotropic models can be considered, and a wide variety of correlation structures. In the second case, models involving spatial weight matrices are covered, such as ''spatial autoregressive models''. The setting is sufficiently general to potentially cover other parametric structures such as certain factor models, and vector-valued observations, and here our preliminary asymptotic theory for parameter estimates is of some independent value. The test statistic is based on a Gaussian pseudo-likelihood ratio, and is shown to have an asymptotic standard normal distribution under the null hypothesis that one of the two models is correct; this limit theory rests strongly on a central limit theorem for the Gaussian pseudo-maximum likelihood parameter estimates. A small Monte Carlo study of finite-sample performance is included.

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“…Whittle (1954) described a spatial random field on R 2 or R 3 by using the stochastic partial differential equation driven by white noise. His work was extended by Heine (1955), Whittle (1956Whittle ( ), (1962, Vecchia (1985Vecchia ( , 1988Vecchia ( , 1992, and Renshaw (1994). Jones and Zhang (1997) consider a separable spatiotemporal random field which is formally written as…”

Section: Stochastic Partial Differential Equationsmentioning

confidence: 99%

Recent developments on the construction of spatio-temporal covariance models

2007

Stoch Environ Res Risk Assess

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Estimation and Model Identification for Continuous Spatial Processes

Cited by 366 publications

References 13 publications

Modeling and spatial prediction of pre-settlement patterns of forest distribution using witness tree data

Modeling and spatial prediction of pre-settlement patterns of forest distribution using witness tree data

Non-nested testing of spatial correlation

Recent developments on the construction of spatio-temporal covariance models

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