On the Intensity Estimation of Poisson Process

Poisson process, homogeneous or inhomogeneous, plays a fundamental role in the theory and application of stochastic process. However, the intensity estimation of inhomogeneous Poisson process remains difficult. In this paper, we summarize three popular technologies for the intensity estimation of Poisson process: smoothing kernel method, Mercer kernel method, as well as Bayesian method. The smoothing kernel method has elegant results for one-dimension stationary data. The RKHS method works by adjusting the kernel functions such that the representer’s theorem can be applied. Similar method also works for data consists of multiple draws from some one-dimension Poisson process. Two Bayesian approached based on the LGCP model and the SGCP model are also discussed.

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