Bayesian Spectrum Analysis and Parameter Estimation (Lecture Notes in Statistics, 48) 1988th Edition by G. Larry Bretthorst (PDF)

Description

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 graduate­ 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 docu­ 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Most people think that spectrum estimation is the same as FFT(Fast Fourier Transform) just because the FFT algorithm has beencelebrated for decades. Bretthorst looks at spectrum estimation from a statisticians point of view. Therefore his view, his examples and his reasoning appeal more to intuition than is usually the case in the electrical engineering text books. To be precise, his approach is Bayesian reasoning. Some people treat this kind of reasoning as heretic because it is based on an unorthodox understanding of probability. While most text books tell you that a probability is a long-run relative frequency, the “Bayesians” think of it as a degree-of-belief (or plausibility).This sounds strange to you ? Yes it is. This book definitely is not in the mainstream. It evolved out of Bretthorst’s PhD thesis (written under E.T. Jaynes, a Bayesian Guru) and it will not surprise you that such a book presents some new material instead of simply summing up well known material. Nevertheless, the book was also meant to be a tutorial introduction to the Bayesian approach. If you have been exposed to some advanced calculus courses, this might be an interesting introduction to statistics for you.Anyway, this book is more than 10 years old now and in the meantime most people would recommend other tutorials into Bayesian statistic, for example the one by D. Sivia (ISBN 0-19-851889-7). END

⭐I wish I had discovered this book long ago. It contains a systematic exposition of the Bayesian approach to the problem of detecting periodic signals. In addition to providing a clear framework for this problem, and many useful results, it is an excellent example of the Bayesian method at work. Just one of the many results obtained early in the book: the relation between the periodogram (which can be veiwed as a frequentist “statistic”) and the Bayesian posterior for this problem is made clear.

⭐Just so folks know, Dr. Bretthorst has published the full volume (now out of print) in pdf form on his website. Best of all is it’s free – thank you Dr. Bretthorst. Do a google search on the title and you can find it.

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