Modelling replicated weed growth data using spatially-varying growth curves

Weed growth in agricultural fields constitutes a major deterrent to the growth of crops, often resulting in low productivity and huge losses for the farmers. Therefore, proper understanding of patterns in weed growth is vital to agricultural research. Recent advances in Geographical Information Systems (GIS) now allow geocoding of agricultural data, which enable more sophisticated spatial analysis. Our current application concerns the development of statistical models for conducting spatial analysis of growth patterns in weeds. Our data comes from an experiment conducted in Waseca, Minnesota, that recorded growth of the weed Setaria spp. We capture the spatial variation in Setaria spp. growth using spatially-varying growth curves. An added challenge is that these designs are spatially replicated, with each plot being a lattice of sub-plots. Therefore, spatial variation may exist at different resolutions - a macro level variation between the plots and micro level variation between the sub-plots nested within each plot. We develop a Bayesian hierarchical framework for this setting. Flexible classes of models result which are fitted using simulation-based methods.