Maximum likelihood estimation for cooperative sequential adsorption

Reference:

Penrose, M. D. and Shcherbakov, V., 2009. Maximum likelihood estimation for cooperative sequential adsorption. Advances in Applied Probability, 41 (4), pp. 978-1001.

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Official URL:

http://dx.doi.org/10.1239/aap/1261669581

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 beta(k) of the current number (k) of points within a specified distance of x. We show that the maximum likelihood estimator of the parameters beta(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.

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