Random point processes in time and space

Donald L. Snyder, Michael I. Miller

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 thrust is point processes on multidimensional spaces, especially to processes 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. Research done by the authors at the Biomedical Computer Laboratory at Washington University has led to newly developed models for position emission tomography and electron-microscopic autoradiography. All the applications which the authors have been involved are examples of nonparametric density estimation, which provides the major motivation for new results on 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. Regularization of the estimates is, therefore, absolutely essential, and knowledge of this subject is crucial.

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[目次]

  • 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.

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この本の情報

書名 Random point processes in time and space
著作者等 Miller, Michael I.
Snyder, Donald L.
Snyder Donald L.
シリーズ名 Springer texts in electrical engineering
出版元 Springer-Verlag
刊行年月 c1991
版表示 2nd ed
ページ数 x, 481 p.
大きさ 24 cm
ISBN 3540975772
0387975772
9781461278214
NCID BA12786235
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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