Customer Reviews

Data Analysis: A Bayesian Tutorial (Oxford Science Publications)

5 star:		(5)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(0)

 

 

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.

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!

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.

This tutorial on Bayesian data analysis is a gem: very terse, yet explaining the concepts very clearly, giving many insightful examples along the way. This is achieved within only 180 pages by focussing on understanding and intuition instead of mathematical formalism. After reading this tutorial, the reader will be familiar with the way of thinking in Bayesian statistics. The tutorial thus encourages the reader to get more independent from the (conceptually more complicated) cook book statistics with the associated risk of misusage. When reading this book I felt as if a whole jumble of more or less unconnected pieces of statistical wisdom was finally falling into place within the Bayesian framework.

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.

This is an excellent tutorial for the both the beginner (undergraduate) and more advanced scientist. Sivia takes the reader through several examples with simple and concise explanations. I have used many of the examples discussed in the book as starting points for problems that I have encountered in my work. I would recommend giving it a try...

Sivia offers a brief but thorough explanation of how to use Bayesians in data analysis. He illustrates with important examples that commonly often arise in the sciences. As in estimating the true amplitude of a signal in the presence of background noise. These days, for anyone in a lab sitting next to an electronic gadget acquiring data, you can surely emphathise with this problem.

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.

Maybe it's just me but I found this book not very helpful. The easy stuff is repeated often (Bayes's theorem is quoted every few pages) but when a difficulty arises it is glossed over. Maybe it gets better: I decided not to finish the book.