Modelling interactions in spatial point patterns : parameter estimation by the maximus likelihood method - Penttinen, Antti (1984)
Markov point processes are a natural family of models for point patterns where the pattern formation is a consequence of interactions between points. The potential function or, alternatively, interaction function is a data summary in such situations. This study comprises models and their use in data analysis. The main problem is the estimation of parametrized potential function from a mapped point pattern data through maximizing the likelihood function. The exact form of the likelihood function is not known for interaction models and therefore, the maximum likelihood estimation must be based on approximations. The emphasis of this study is in sparse data approximations and on the other hand in simulation-based (Monte Carlo) approximations of the likelihood function. The main result is the use of the efficient score stochastic process in the approximation of the maximum likelihood solution. The method is illustrated by an empirical example where interactions in waterstrider populations have been modelled.