An efficient maximum entropy approach for categorical variable prediction

We address the problem of the prediction of a spatial categorical variable by revisiting the maximum entropy approach. We first argue that, for predicting category probabilities, a maximum entropy approach is more natural than a least-squares approach, such as (co-)kriging of indicator functions. We then show that, knowing the categories observed at surrounding locations, the conditional probability of observing a category at a location obtained with a particular maximum entropy principle is a simple combination of sums and products of univariate and bivariate probabilities. This prediction equation can be used for categorical estimation or categorical simulation. We make connections to earlier work on prediction of categorical variables. On simulated data sets we show that our equation is a very good approximation to Bayesian maximum entropy (BME), while being orders of magnitude faster to compute. Our approach is then illustrated by using the celebrated Swiss Jura data set.