CoxProzesse
Cox processes, also known as doubly stochastic Poisson processes, are a class of point processes in which the instantaneous intensity function is itself a random process. In a Cox process, once the random intensity Λ(t) is realized, the points form a Poisson process with rate Λ(t). Unconditionally, the process is a mixed Poisson process, because the Poisson randomness is compounded by the randomness of Λ.
Mathematically, if Λ(t, ω) is a nonnegative, adapted stochastic process on a probability space, then conditional on
A common and flexible subfamily is the log-Gaussian Cox process (LGCP), where Λ(t) = exp(G(t)) and G(t)
Applications of Cox processes span ecology, epidemiology, geology, astronomy, and finance, among others, wherever spatial or
Inference for Cox processes often relies on conditioning on Λ and integrating it out, which leads to