Random point processes in time and space
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Bibliographic Information
Random point processes in time and space
（Springer texts in electrical engineering）
Springer-Verlag, c1991
2nd ed
- : us
- : gw
- : pbk
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Note
Rev. ed. of: Random point processes. 1975
Includes bibliographical references and indexes
Description and Table of Contents
- Volume
-
: us ISBN 9780387975771
Description
This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro- cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re- luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models.
Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo- ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.
Table of Contents
1 Point and Counting Processes: Introduction and Preliminaries.- 1.1 Introduction.- 1.2 Counting Processes.- 1.3 Organization of the Book.- 1.4 Mathematical Preliminaries.- 1.5 References.- 2 Poisson Processes.- 2.1 Introduction.- 2.2 Conditions for Temporal Poisson-Processes.- 2.3 Point-Location Statistics.- 2.4 Parameter Estimation for Temporal Poisson-Processes.- 2.5 Multidimensional Poisson-Processes.- 2.6 References.- 2.7 Problems.- 3 Translated Poisson-Processes.- 3.1 Introduction.- 3.2 Statistics of Translated Poisson-Processes.- 3.3 Estimation for Translated Poisson-Processes.- 3.4 Constrained Estimation.- 3.5 Conclusions.- 3.6 References.- 3.7 Problems.- 4 Compound Poisson-Processes.- 4.1 Introduction.- 4.2 Statistics of Compound Poisson-Processes.- 4.3 Representation of Compound Poisson-Processes.- 4.4 Estimation for Compound Poisson-Processes.- 4.5 Statistical Inference for Mixed Poisson-Processes.- 4.6 References.- 4.7 Problems.- 5 Filtered Poisson-Processes.- 5.1 Introduction.- 5.2 Superposition of Point Responses.- 5.3 Poisson Driven Markov Processes.- 5.4 References.- 5.5 Problems.- 6 Self-Exciting Point Processes.- 6.1 Introduction.- 6.2 General Self-Exciting Point Processes.- 6.3 Self-Exciting Point Processes with Limited Memory.- 6.4 References.- 6.5 Problems.- 7 Doubly Stochastic Poisson-Processes.- 7.1 Introduction.- 7.2 Counting Statistics.- 7.3 Time Statistics.- 7.4 Filtering.- 7.5 Doubly Stochastic Multidimensional Poisson-Processes.- 7.6 References.- 7.7 Problems.- Author Index.- Examples Index 473.- Subject Index 477.
- Volume
-
: pbk ISBN 9781461278214
Description
This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.
Table of Contents
1 Point and Counting Processes: Introduction and Preliminaries.- 1.1 Introduction.- 1.2 Counting Processes.- 1.3 Organization of the Book.- 1.4 Mathematical Preliminaries.- 1.5 References.- 2 Poisson Processes.- 2.1 Introduction.- 2.2 Conditions for Temporal Poisson-Processes.- 2.3 Point-Location Statistics.- 2.4 Parameter Estimation for Temporal Poisson-Processes.- 2.5 Multidimensional Poisson-Processes.- 2.6 References.- 2.7 Problems.- 3 Translated Poisson-Processes.- 3.1 Introduction.- 3.2 Statistics of Translated Poisson-Processes.- 3.3 Estimation for Translated Poisson-Processes.- 3.4 Constrained Estimation.- 3.5 Conclusions.- 3.6 References.- 3.7 Problems.- 4 Compound Poisson-Processes.- 4.1 Introduction.- 4.2 Statistics of Compound Poisson-Processes.- 4.3 Representation of Compound Poisson-Processes.- 4.4 Estimation for Compound Poisson-Processes.- 4.5 Statistical Inference for Mixed Poisson-Processes.- 4.6 References.- 4.7 Problems.- 5 Filtered Poisson-Processes.- 5.1 Introduction.- 5.2 Superposition of Point Responses.- 5.3 Poisson Driven Markov Processes.- 5.4 References.- 5.5 Problems.- 6 Self-Exciting Point Processes.- 6.1 Introduction.- 6.2 General Self-Exciting Point Processes.- 6.3 Self-Exciting Point Processes with Limited Memory.- 6.4 References.- 6.5 Problems.- 7 Doubly Stochastic Poisson-Processes.- 7.1 Introduction.- 7.2 Counting Statistics.- 7.3 Time Statistics.- 7.4 Filtering.- 7.5 Doubly Stochastic Multidimensional Poisson-Processes.- 7.6 References.- 7.7 Problems.- Author Index.- Examples Index 473.- Subject Index 477.
- Volume
-
: gw ISBN 9783540975779
Description
This senior graduate level textbook is the second revised edition of the textbook "Random Point Processes", written by D.L.Snyder and published in 1975. Its main subject area is point processes on multidimensional spaces, especially processes in two dimensions, reflecting the increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. Research done by the authors at the Biomedical Computer Laboratory at Washington University has resulted in newly developed models for position emission tomography and electron-microscopic autoradiography. All the applications are examples of nonparametric density estimation, which help provide new results concerning constrained estimation techniques. For these applications, the use of unconstrained maximum-likelihood estimation fails because the estimates are not consistent in the statistical sense; they do not converge, with increasing amounts of data, towards the quantity being estimated and regularization of the estimates is therefore considered essential.
This graduate textbook on communications, signal processing and numerical mathematics is intended for the use of graduate students, researchers and practising engineers.
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