When fitting a model to data, one would ideally like to use maximum likelihood estimation, due to its nice statistical properties. Unfortunately, the likelihood function of a general Gibbs point process is typically not tractable, due to the associated normalizing constant. This has led to the development of a range of alternative methods, such as Takacs-Fiksel estimation (including its special case pseudolikelihood estimation) and Point Process Learning.

Leveraging recent probabilistic results for Gibbs processes, in this talk we present an approach to perform approximate likelihood estimation for Gibbs processes. Specifically, we show that the likelihood function can be expressed completely in terms of the Papangelou conditional intensity, which is typically known and tractable. This new likelihood representation involves an infinite series expansion, and we discuss different ways of approximating it, and thereby the likelihood function. We further discuss how this plays out in certain models and compare it to the state-of-the-art.