  Deriving exact density functions for Gibbs point processes has been
challenging due to their general intractability, stemming from the
intractability of their normalising constants/partition functions. This paper
offers a solution to this open problem by exploiting a recent alternative
representation of point process densities. Here, for a finite point process,
the density is expressed as the void probability multiplied by a higher-order
Papangelou conditional intensity function. By leveraging recent results on
dependent thinnings, exact expressions for generating functionals and void
probabilities of locally stable point processes are derived. Consequently,
exact expressions for density/likelihood functions, partition functions and
posterior densities are also obtained. The paper finally extends the results to
locally stable Gibbsian random fields on lattices by representing them as point
processes.
