- Series: Oxford Science Publications
- Paperback: 208 pages
- Publisher: Oxford University Press (September 26, 1996)
- Language: English
- ISBN-10: 0198518897
- ISBN-13: 978-0198518891
- Product Dimensions: 6.1 x 0.3 x 9.2 inches
- Shipping Weight: 10.6 ounces (View shipping rates and policies)
- Average Customer Review: 8 customer reviews
- Amazon Best Sellers Rank: #1,769,965 in Books (See Top 100 in Books)
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Data Analysis: A Bayesian Tutorial (Oxford Science Publications)
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"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.
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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.
The necessary background for his book includes being familiar with multivariable calculus. Specifically, with the Taylor expansion in several variables, and with the Jacobian matrix of second partial derivatives. Plus of course a grounding in statistics, including maximum likelihood estimations and the normal distribution.
A few critical remarks: (1) A clearer structure with more informative section and subsection headings would help to quicker find things and keep the material orderly in one`s mind. (As an example, the two core chapters are entitled Parameter estimation I" and Parameter estimation II"). (2) The chapter on non-paramteric estimation is much harder to understand than the first six chapters. This is in part justified by the advancedness of the topic but it could profit from a streamlining (and updating). (3) This book certainly would have the chance to become much more popular than it is now if it was more reasonably priced.
The reader should have a firm command of elementary probability theory, first year calculus (Taylor expansion, multidimensional integration, finding the maximum of a multi-variable function), as well as elementary linear algebra (diagonalization, eigenvectors, determinants). Ideally, she should be familiar with basic classical statistics, as this will make her appreciate the elegance of the Bayesian view more. Physicists will love this book.