This article develops a set of tools for smoothing and prediction with dependent point event patterns. The methodology is motivated by the problem of tracking weekly maps of violent crime events, but ...

A U-statistic of a Poisson point process is defined as the sum ∑ f (x₁, · · ·, xk) over all (possibly infinitely many) k-tuples of distinct points of the point process. Using the Malliavin calculus, ...