scholarly journals On identifiability and consistency of the nugget in Gaussian spatial process models

2021 ◽  
Author(s):  
Wenpin Tang ◽  
Lu Zhang ◽  
Sudipto Banerjee
Keyword(s):  
Process Models ◽  
Spatial Process ◽  
Gaussian Spatial Process

Application and comparison of spatial models in analyzing tree-genetics field trials

1990 ◽  
Vol 20 (5) ◽  
pp. 536-546 ◽  
Author(s):  
Steen Magnussen
Keyword(s):  
Classical Model ◽  
Substantial Reduction ◽  
Spatial Models ◽  
Tree Height ◽  
Process Models ◽  
Spatial Process ◽  
Spatial Analyses ◽  
Spatial Covariance ◽  
Significant Difference ◽  
Tree Genetics

Tree height of jack pine full-sib families, originating from all possible combinations of three parental provenances and growing on three sites, was analyzed with 1 classical model and 11 nearest-neighbour spatial process models. Extension of the classical linear model with spatial interaction terms was deemed necessary in light of significant neighbourhood correlations among effect-free observations (residuals) on two of the three sites. The strength and extent of spatial and temporal correlations are demonstrated in both visual and tabular form. Only 4 of the 11 spatial models provided a substantial reduction (5–20%) in the significant difference between two estimates of full-sib family tree height. Spatial adjustments averaged 1–3% at the family level, with few families adjusted by more than 10%. The cumulative (temporal) effect of spatial covariance was demonstrated in rank correlations between adjusted and observed family means. No simple trends were obtained when adjusted variance components and heritabilities were compared with their unadjusted counter-parts, but most models tended to deflate genetic effects and reduce heritabilities. It is concluded that although spatial analyses provide an attractive tool for the experimenter, the lack of a cause and effect hypothesis in forest genetic trials necessitates model searching without the guarantee of true treatment effects. Spatial analysis provides good indicators of the need to collect additional site information for more powerful analyses. Careful planning and intensive site preparation may greatly reduce spatial covariances and the need for spatial analyses.

scholarly journals Translating environmental xenobiotic fate models across scales

1997 ◽  
Vol 1 (4) ◽  
pp. 895-904 ◽  
Author(s):  
O. Richter ◽  
B. Diekkrüger
Keyword(s):  
Stochastic Models ◽  
Process Models ◽  
Spatial Process ◽  
Soil Parameters ◽  
Deterministic Models ◽  
Deterministic Process ◽  
Statistical Variation ◽  
Scale Models ◽  
Classical Models ◽  
Environmental Xenobiotic

Abstract. The classical models developed for degradation and transport of xenobiotics have been derived with the assumption of homogeneous environments. Unfortunately, deterministic models function well in the laboratory under homogeneous conditions but such homogeneous conditions often do not prevail in the field. A possible solution is the incorporation of the statistical variation of soil parameters into deterministic process models. This demands the development of stochastic models of spatial variability. To this end, spatial soil parameter fields are conceived as the realisation of a random spatial process. Extrapolation of local fine scale models to large heterogeneous fields is achieved by coupling deterministic process models with random spatial field models.

Directional Rates of Change Under Spatial Process Models

2003 ◽  
Vol 98 (464) ◽  
pp. 946-954 ◽  
Author(s):  
Sudipto Banerjee ◽  
Alan E Gelfand ◽  
C. F Sirmans
Keyword(s):  
Process Models ◽  
Spatial Process ◽  
Rates Of Change

scholarly journals Hierarchical Spatial Process Models for Multiple Traits in Large Genetic Trials

2010 ◽  
Vol 105 (490) ◽  
pp. 506-521 ◽  
Author(s):  
Sudipto Banerjee ◽  
Andrew O. Finley ◽  
Patrik Waldmann ◽  
Tore Ericsson
Keyword(s):  
Process Models ◽  
Spatial Process ◽  
Multiple Traits
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