Maximum likelihood estimation for cooperative sequential adsorption

Abstract

We consider a model for a time series of spatial locations, in which points are placed sequentially at random into an initially empty region of ℝ d , and given the current configuration of points, the likelihood at location x for the next particle is proportional to a specified function β k of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters β k (assumed to be zero for k exceeding some fixed threshold) is consistent in the thermodynamic limit where the number of points grows in proportion to the size of the region.