When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say β̂, can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of β̂ except in some speci...

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...

Introduction It is usually assumed that photon events, as X-ray photons observed by a satellite, may be described by the theory of point processes (cf e. g. Matsuo, Teich and Saleh, 1983). The simplest and most common process is the homogeneous Poisson point process. Photons are usually generated in a Poisson process and in addition to that, the detection of photons is a Poisson process too. In...

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...

This paper presents some general formulas for random partitions of a finite set derived by Kingman’s model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the ...

A celebrated theorem of Burke’s asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d. services of finite mean, but otherwise of arbitrary distribu...

In some recent work it has been shown how to solve optimal stopping problems approximatively for independent sequences and also for some dependent sequences, when the associated embedded point processes converge to a Poisson process. In this paper we extend these results to the case where the limit is a Poisson cluster process with random or with deterministic cluster. We develop a new method o...

A factor graph of a point process is a graph whose vertices are the points of the process, and which is constructed from the process in a deterministic isometry-invariant way. We prove that the d-dimensional Poisson process has a one-ended tree as a factor graph. This implies that the Poisson points can be given an ordering isomorphic to the usual ordering of the integers in a deterministic iso...

In this paper, we revisit the original ideas of Stein and propose an estimator of the intensity parameter of a homogeneous Poisson point process defined on Rd and observed on a bounded window. The procedure is based on a new integration by parts formula for Poisson point processes. We show that our Stein estimator outperforms the maximum likelihood estimator in terms of mean squared error. In m...