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UBC Theses and Dissertations

An approximate spatio-temporal Bayesian model for Alberta wheat yield Popoff, Evan


Crop forecasting models are very valuable to a number of agricultural and government agencies. We investigated the effect of spatial and temporal environmental climate covariates on the growth of crop yield (wheat) at the regional scale across the province of Alberta. Model fitting was accomplished using data collected during the growing season from climate stations across Alberta provided by Agriculture and Agri-Food Canada (AAFC). A best fitting model was selected which takes into account simplicity (number of covariates used) and accuracy (predictive capability based on two selection criteria). There have been a number of Bayesian methods for predicting wheat yield. However, many of these methods typically involve extensive algorithms such as a Metropolis-Hastings Markov Chain Monte Carlo (MCMC) that adds substantial computational complexity and run-time. We investigated the application of a spatio-temporal Bayesian model entitled the Integrated Nested Laplace Approximation (INLA). This method offers a computationally cheaper alternative to the MCMC approach and is capable of handling large data requiring interpolation (data sparsity) with relative ease. By structuring the model to have a sparse precision matrix, INLA is able to simplify posterior marginal estimation of the parameters by incorporating the Laplace approximation. The INLA model demonstrated strong predictive capabilities when predicting for one year in advance or hind-casting for a it single previous year. However, when multiple years of data were removed or predictions were made for multiple years in advance, INLA struggled to make predictions which deviated considerably from the mean of the remaining data. Predictive performance in the best fitting model saw a 40% increase in root mean squared error (RMSE) when moving from one year to two and another 6% increase when moving from two to three years. We conclude that the INLA model structure offers valuable information when examining one year in advance but caution should be taken when attempting to forecast for multiple years in advance.

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