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AuthorBretthorst, G. Larry. author
TitleBayesian Spectrum Analysis and Parameter Estimation [electronic resource] / by G. Larry Bretthorst
ImprintNew York, NY : Springer New York : Imprint: Springer, 1988
Connect tohttp://dx.doi.org/10.1007/978-1-4684-9399-3
Descript XII, 209 p. online resource

SUMMARY

This work is essentially an extensive revision of my Ph.D. dissertation, [1J. It 1S primarily a research document on the application of probability theory to the parameter estimation problem. The people who will be interested in this material are physicists, economists, and engineers who have to deal with data on a daily basis; consequently, we have included a great deal of introductory and tutorial material. Any person with the equivalent of the mathematics background required for the graduateยญ level study of physics should be able to follow the material contained in this book, though not without eIfort. From the time the dissertation was written until now (approximately one year) our understanding of the parameter estimation problem has changed extensively. We have tried to incorporate what we have learned into this book. I am indebted to a number of people who have aided me in preparing this docuยญ ment: Dr. C. Ray Smith, Steve Finney, Juana Sunchez, Matthew Self, and Dr. Pat Gibbons who acted as readers and editors. In addition, I must extend my deepest thanks to Dr. Joseph Ackerman for his support during the time this manuscript was being prepared


CONTENT

1 Introduction -- 2 Single Stationary Sinusoid Plus Noise -- 3 The General Model Equation Plus Noise -- 4 Estimating the Parameters -- 5 Model Selection -- 6 Spectral Estimation -- 7 Applications -- 8 Summary and Conclusions -- A Choosing a Prior Probability -- B Improper Priors as Limits -- C Removing Nuisance Parameters -- D Uninformative Prior Probabilities -- E Computing the โ{128}{156}Student t-Distributionโ{128}{157}


Mathematics Applied mathematics Engineering mathematics Mathematics Applications of Mathematics



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