Consistency of likelihood estimation for Gibbs point processes
证明了参数吉布斯点过程模型最大似然估计的强一致性，涵盖多种交互类型和参数形式，并推导了Strauss、Lennard-Jones等具体模型的一致性。
Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard–Jones model and the area-interaction model.