Name
Abstract | ||
|---|---|---|
A space-time point process is a stochastic process having as realizations points with random coordinates in both space and time. We define a general class of space-time point processes which we term {em analytic}. These are point processes that have only finite numbers of points in finite time intervals, absolutely continuous joint-occurrence distributions, and for which points do not occur with certainty in finite time intervals. Analytic point processes possess an intensity determined by the past of the point process. As a class, analytic point processes remain closed under randomization by a parameter. The problem we consider is that of estimating a random parameter of an observed space-time point process. This parameter may be drawn from a function space and can, therefore, model a random variable, random process, or random field that influences the space-time point process. Feedback interactions between the point process and the randomizing parameter are included. The conditional probability measure of the parameter given the observed space-time point process is a sufficient statistic for forming estimates satisfying a wide variety of performance criteria. A general representation for this conditional measure is developed, and applications to filtering, smoothing, prediction, and hypothesis testing are given. |
Year | DOI | Venue |
|---|---|---|
1976 | 10.1109/TIT.1976.1055558 | IEEE Transactions on Information Theory |
Keywords | Field | DocType |
Parameter estimation,Point processes | Stochastic geometry,Determinantal point process,Combinatorics,Random field,Point process,Stochastic process,Moment measure,Poisson point process,Nearest neighbour distribution,Mathematics | Journal |
Volume | Issue | ISSN |
22 | 3 | 0018-9448 |
Citations | PageRank | References |
5 | 1.60 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| P. Fishman | 1 | 5 | 1.60 |
| D. Snyder | 2 | 112 | 40.42 |