A Bayesian analysis of an agricultural field trial with three spatial dimensions
Donald, Margaret, Alston, Clair L., Young, Rick R. , & Mengersen, Kerrie L. (2011) A Bayesian analysis of an agricultural field trial with three spatial dimensions. Computational Statistics & Data Analysis, 55(12), pp. 3320-3332.
Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions.
The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package.
The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.
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|Item Type:||Journal Article|
|Divisions:||Current > Schools > School of Mathematical Sciences|
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Copyright 2011 Elsevier|
|Copyright Statement:||NOTICE: this is the author’s version of a work that was accepted for publication in [Computational Statistics & Data Analysis]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [Computational Statistics & Data Analysis], [VOL 55, ISSUE 2, (2011)] 10.1016/j.csda.2011.06.022|
|Deposited On:||02 Feb 2012 15:03|
|Last Modified:||04 Feb 2012 00:58|
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