Data Analysis: A Bayesian Tutorial (Oxford Science Publications) [Paperback]

D. S. Sivia (Author)

Book Description

Publication Date: September 26, 1996 | ISBN-10: 0198518897 | ISBN-13: 978-0198518891

This is the first book on the maximum entropy and Bayesian methods aimed at senior undergraduates in science and engineering. It takes the mystery out of statistics by showing how a few fundamental rules can be used to tackle a wide variety of problems in data analysis. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy, and experimental design. As a logical and unified approach to the subject of data analysis, with a self-contained tutorial approach, this work will be valued by instructors and students alike.

Editorial Reviews

Review

"This book is designed to be a guide to the Bayesian approach. It is certainly not an all-encompassing textbook on the subject but rather describes for the reader how one can use the Bayesian approach for standard data analyses. . . .Well written and at a modest technical level (senior undergraduate)." --Technometrics

"Sivia's tutorial explains the Bayesian approach for analyzing experimental data. In particular, stress is placed on modern developments such as maximum entropy."--Choice

About the Author

D. S. Sivia, Rutherford Appleton Laboratory and St Catherine's College, Oxford.

Product Details

• Paperback: 208 pages
• Publisher: Oxford University Press, USA (September 26, 1996)
• Language: English
• ISBN-10: 0198518897
• ISBN-13: 978-0198518891
• Product Dimensions: 9.1 x 5.9 x 0.7 inches
• Shipping Weight: 10.6 ounces
• Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #1,676,018 in Books (See Top 100 in Books)
  • #49 in Books > Professional & Technical > Professional Science > Physics > Entropy

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Customer Reviews

Most Helpful Customer Reviews

65 of 68 people found the following review helpful:

5.0 out of 5 stars Self-contained and readable tutorial guide, April 2, 2000

By 

Juergen Kahrs (Bremen, Germany) - See all my reviews
(REAL NAME)   

This review is from: Data Analysis: A Bayesian Tutorial (Oxford Science Publications) (Paperback)

Mathematics looks like a pile of abstract facts, axioms and theoremsto most people. It is hard to imagine that in some branches of mathematics, there are unsettled controversies about the meanings of basic notions like probability. Statistics is one of these branches, where professional researchers and lecturers can be divided into some sort of "schools of thought".

This small book of 189 pages is a tutorial introduction into statistics. It addresses senior undergraduates and research students in science and engineering. If symbols like integrals, factorials or notions like Eigenvalues do frighten you, you should first complete some courses on calculus and algebra before reading this book. Contrary to "classic" text books on statistics, this book employs the so called Bayesian understanding of probability. While the classic understanding of probability sees each probability as a long-run relative frequency, the Bayesian school sees it as a degree-of-belief (or plausibility). This may sound like a minor disagreement, but it leads to very different ways of solving problems.

Throughout the book, the author explains seven examples of increasing complexity to the reader and solves the problems. Especially in the first two chapters, he simplifies his favourite applications of probability theory in order to explain basic concepts like probability, the error-bar, correlation, and marginal distributions. Each of the graphical panels is explained in detail to make it easier to understand the intuitive meaning of concepts like the probability density function. Often, the author also mentions common misconceptions and vividly explains the consequences of such misunderstandings.

Having read this book, you will be able to employ probability theory in scientific and engineering work. For example in estimation of a parameter like a scattering angle. While these results are often very useful in practice, you should be warned that the Bayesian approach might annoy some representatives of the orthodox statistical guild.

Nevertheless, the book is a good tutorial which is worth reading.

33 of 35 people found the following review helpful:

5.0 out of 5 stars This is how a statistics book ought to be written!, October 26, 2000

By 

Pieter van Gelder (Delft, NL) - See all my reviews

This review is from: Data Analysis: A Bayesian Tutorial (Oxford Science Publications) (Paperback)

Sivia shows in the first part of his compact book (189 pages) very nice examples (such as the lighthouse problem, signal amplitudes in presence of background noise, etc) how the Bayesian theory works out. The kangaroo problem and monkey argument come up to explain the maximum entropy theory. Further on in the book examples are given in the area of DSP (digital signal processing) and on experimental design, added with references to Sivia's Bayesian applications in molecular spectroscopy, neutron scattering - and powder diffrication analysis. As an applied statistician within the area of hydrological engineering (flood frequency analysis), it was very fruitful to read Sivia's book to fresh up the way of thinking... I highly recommend the book to other applied statisticians!

18 of 20 people found the following review helpful:

5.0 out of 5 stars Learn what it means to be a "Bayesian", September 14, 2004

By 

K. Huyser (Mtn View, CA USA) - See all my reviews

This review is from: Data Analysis: A Bayesian Tutorial (Oxford Science Publications) (Paperback)

For years I listened to people present "Bayesian" solutions to problems without appreciating the subtler implications of the term. Bayes' theorem is one of the first topics taught in freshman-level probability and statistics. It's taught, and it's used, but it isn't a central part of the teaching of modern statistics.

Bayesians make it central. Sivia does a masterful job of deriving most of statistics from judicious applications of Bayes' theorem. He can do this, in part, because the visible universe is finite. Infinities and limit theorems can be bypassed, and previously impossible functional forms become workable.

The book is a tutorial; you have to think. But it's well worth it.