Analysis of spatial count data using Kalman smoothing

We consider spatial count data from an agricultural field experiment. Counts of weed plants in a field have been recorded in a project on precision farming. Interest is in mapping the weed intensity so that the dose of herbicide applied at any location can be adjusted to the amount of weed present at the location. We elaborate on a link between state space models and Markov random fields. The observations are modelled as independent Poisson counts conditional on a Gaussian Markov random field. We employ the fact that the model may be written as a state space model which may be analysed by combining approximate Kalman filter techniques with importance sampling.