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Case Studies in Bayesian Statistical Modelling and Analysis by Anthony N. Pettitt, Kerrie L. Mengersen, Clair L. Alston

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14

Moisture, Crops and Salination: An Analysis of a Three-Dimensional Agricultural Data Set

Margaret Donald1, Clair L. Alston1, Rick Young2 and Kerrie L. Mengersen1

1Queensland University of Technology, Brisbane, Australia

2Tamworth Agricultural Institute, Department of Primary Industries, Tamworth, Australia

14.1 Introduction

Large data sets over space and time are generated routinely by modern technology. Such data typically exhibit high autocorrelations over both spatial and time dimensions. We describe a WinBUGS application for a spatial three-dimensional data set in which conditional autoregressive (CAR) models are used for point-referenced data to account for spatial autocorrelations.

The CAR model was originally suggested by Besag (1974) in the context of image analysis and is also known as the intrinsic CAR model with a convolution prior, or the Besag, York and Mollie (BYM) model. It is used here, rather than the geostatistical models usually suggested for point-referenced data (Banerjee et al. 2004; Cressie 1991), because we found such models effectively impossible to fit in WinBUGS when there was a regression component with a large number of terms. This is not surprising since CAR models have a sparse precision matrix whereas geostatistical models do not. The CAR model is an example of a Gaussian Markov random field (GMRF).

There are two key elements to the analyses presented. Although the measurements are collected sufficiently closely across space to expect autocorrelation, ...

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