Parameter estimation methods for random point fields with local interactions

• Main Author: P. Ya. Grabarnik
• Format: Article
• Language: Russian
• Published: Institute of Computer Science 2016-04-01
• Series: Компьютерные исследования и моделирование
• Subjects: Gibbs point process; estimating function; pseudo-likelihood; parametric inference
• Online Access: http://crm.ics.org.ru/uploads/crmissues/crm_2016_2/16.08.10.pdf

The paper gives an overview of methods for estimating the parameters of random point fields with local interaction between points. It is shown that the conventional method of the maximum pseudo-likelihood is a special case of the family of estimation methods based on the use of the auxiliary Markov process, invariant measure of which is the Gibbs point field with parameters to be estimated. A generalization of this method, resulting in estimating equation that can not be obtained by the the universal Takacs-Fiksel method, is proposed. It is shown by computer simulations that the new method enables to obtain estimates which have better quality than those by a widely used method of the maximum pseudolikelihood.