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Ng, T. L. and Murphy, T. B. (2019), Estimation of the intensity function of an inhomogeneous Poisson process with a change‐point. Can J Statistics, 47: 604-618. doi: 10.1002/cjs.11514
Inhomogeneous Poisson processes are used to model various random phenomena in applied fields including reliability, biology and natural disasters. The estimation of the intensity of inhomogeneous Poisson processes has attracted significant attention in statistics and machine learning. Existing approaches typically assume that the intensity function is continuous; this assumption implies that, for example, the reliability of a system evolves continuously over time. In many cases, however, the reliability of a system, after an intervention such as a repair, may be different to that before the intervention. In such cases, it is more appropriate to model the process using an inhomogeneous Poisson process with change-points in the intensity.
This paper develops a nonparametric Bayesian approach to estimating the intensity function with a single change-point at an unknown time. Posterior convergence properties under general prior setting and the special case of a Gaussian process prior are studied. Posterior consistency ensures that the posterior distribution of the intensity function will be increasingly concentrated around the true intensity function as more count processes are observed.
The performance of the approach is evaluated using simulation studies and real world applications.