Estimating Spline-Based Nonhomogeneous Poisson Intensities Using Constrained Quadratic Programming

This paper estimates the intensity function of a nonhomogeneous Poisson process (NHPP) using a spline-based method with constrained quadratic programming (CQP). Based on the property of B-splines, we transform the estimation problem into an optimization problem and apply CQP to obtain the estimated intensity function with low computational expense. Numerical experiments are conducted to verify the performance of our method. In addition, the impacts of the number of intervals from event-count data and the number of knots in B-splines are also discussed to explore the properties of spline-based models.