Statistical inference for random point fields of a Markov type and its application in forest ecology

We review models of random point fields which describe systems of spatial distributed interacting objects. These models have been used in many of areas of science, for instance, seismology, ecology, forestry, geography, spatial epidemiology, medicine. We focus on models defined by the density with respect to the Poisson point process. Markov property of random point fields with a neighbourhood relation which may depend on points of a pattern is considered.
Models of spatial random systems of point objects are viewed from perspective of stochastic geometry and spatial statistics which operate with datasets of relatively small sizes. Main interest is in methods which enable to estimate model parameters in situations when classical approaches are not applicable. We report properties of a new estimation procedure which can be thought of as a modification of the maximum pseudo-likelihood method. We have investigated performance of the new estimator by a simulation experiment and concluded that its quality is better than the maximum pseudo-likelihood estimator. Besides, the proposed method allows for implementation by standard statistical packages.
Application of statistical methods and models is illustrated by practical examples from forest ecology.