Precise identification of the time when a process has changed enables process engineers to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for a Poisson process in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step < /div> change, a linear trend and a known multip...

in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

in order to study the relationship between random boolean sets and some explanatory variables, this paper introduces a propagation model. this model can be applied when corresponding poisson process of the boolean model is related to explanatory variables and the random grains are not affected by these variables. an approximation for the likelihood is used to find pseudo-maximum likelihood esti...

On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on R. We examine the local weak convergence of the navigation tree, the asymptotic average of a func...

Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...

In this paper we consider the most visited site, Xt, of a Poisson process up to time t. Our point of departure from the literature on maximal spacings is our asymptotic analysis of where the maximal spacing occurs (i.e., the size of Xt) and not the size of the spacings.