Non-homogeneous Poisson process intensity modeling and estimation using measure transport

Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to health sciences. Often, central object interest point process is underlying intensity function. Here, we present general model for function non-homogeneous using measure transport. The built flexible bijective mapping that maps simpler reference We enforce bijectivity by modeling map as composition multiple have increasing triangular structure, and show exhibits an important approximation property. Estimation accomplished within optimization framework, wherein computations efficiently done tools originally designed facilitate deep learning, graphics processing unit. Point simulation uncertainty quantification straightforward do with proposed model. demonstrate potential benefits our method over conventional approaches through various studies. also illustrate use on real data set containing locations seismic events near Fiji since 1964.