Bayesian inference of spatially correlated random parameters for on-farm experiment
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Accounting for spatial variability is crucial while estimating treatment effects in large on-farm trials. It allows to determine the optimal treatment for every part of a paddock, resulting in a management strategy that improves sustainability and profitability of the farm. We specify a model with spatially correlated random parameters to account for the spatial variability in large on-farm trials. A Bayesian framework has been adopted to estimate the posterior distribution of these parameters. By accounting for spatial variability, this framework allows the estimation of spatially-varying treatment effects in large on-farm trials. Several approaches have been proposed in the past for assessing spatial variability. However, these approaches lack an adequate discussion of the potential problem of model misspecification. Often the Gaussian distribution is assumed for the response variable, and this assumption is rarely investigated. Using Bayesian post sampling tools, we show how to diagnose the problem of model misspecification. To illustrate the applicability of our proposed method, we analysed a real on-farm strip trial from Las Rosas, Argentina, with the main aim of obtaining a spatial map of locally-varying optimal nitrogen rates for the entire paddock. The analysis of these data revealed that the assumption of Gaussian distribution for the response variable is unsatisfactory; the Student-t distribution provides a more robust inference. We finish the paper by discussing the difference between the proposed Bayesian approach and geographically weighted regression, and comparing the results of these two approaches.
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