UC San Diego

We investigate methods for resampling inhomogeneous marked point processes, focusing on Poisson point processes. In Chapter 1 we introduce the problem and provide some background information. In Chapter 2 we adapt existing methods for resampling homogeneous marked point processes to the case of one-dimensional inhomogeneous marked point processes data. In Chapter 3 we extend theoretical results such as asymptotic normality from the homogeneous to the inhomogeneous setting. In Chapter 4 we establish the validity of our local block bootstrap procedure for one- dimensional inhomogeneous marked point processes data while in Chapter 5 we compare the performance of the one- dimensional methods. In Chapter 6 and Chapter 7, we extend the theory and validity of our local block bootstrap procedure to higher dimensions. We carry out simulations to test the performance of our methods under varying distributions of points as well as varying dependencies on the associated marks