Supplementary Material for Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes
نویسندگان
چکیده
Appendix A. There exists a Cox process with an a.s. C ∞ intensity coinciding with any finite dimensional prior. In this section we prove the proposition below. Proposition .1 Let Q be an (n + 1) dimensional continuous probability distribution whose density has support n+1 i=1 ]0, +∞[, and let x 1 ,. .. , x n be n points on a compact domain S ⊂ R d. There exists an almost surely non-negative and C ∞ stochastic process λ on S such that a random draw. Let us denote x j , j ≤ d the j-th coordinate of x ∈ R d. We consider the family of functions parametrized by α ∈ R:
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