Data Analysis —— A Bayesian Tutorial

This is an excellent read for scientists and engineers who are interested in approaching data analysis from the perspective of making predictions using probability density functions (pdf) informed from the state of one's knowledge. In other words, the simple math behind Bayes theorem and marginalization gives rise to probability predictions using likelihood (data model) pdf, prior (i.e, best guess of degrees of freedom in the model) pdf, and if needed, evidence/marginal (domain of model) pdf. The book essential discusses this in a few different areas, namely: Single Parameter estimation, ex., probability of the mean of some data set Multi-parameter estimation Model comparison, ex., the probability that M parameters describe data. Selecting pdf and MaxEntropy, i.e., which pdf provides the most information for given data. Inference, i.e., functional model estimation Least-squares Computational approaches to the calculation of posterior pdf The first several chapters in the book are more of a survey and primer than a workbook, it gets you thinking about how to do data analysis from a probabilistic standpoint and provides some case studies/examples but doesn't give much of the "mechanics" for how to do things except for the last few chapters. Overall a good first book to read with regard to Bayesian methods.

Good introductory book an Bayesian statistics. Concise and quite complete, requires some background in calculus but very accessible book.

It's hard to get through some chapters. I guess it' rather me. I think book need fair understand of some math and probability but it is very good book.

Bought the "Kindle" version, my Kindle oasis says it's not supported on this device... I can read it on my iPad though. Annoying..

One of my favourites. Well written, good book.

As a physics student I was frustrated by statistics with its apparent lack of conceptual foundation and the toolbox approach to data analysis. A little more than 15 years ago, I picked up the first edition of this book and learned Bayesian data analysis from it. The topic is introduced from a practical perspective designed for someone who wants to use these methods for data analysis applied to real problems. This relatively small book clearly, cogently, and pleasantly covers the concepts, the theory and practice. I was pleased to be able to use this text to guide me in applying Bayesian data analysis methods to my own problems. Today, as an experienced practitioner, I find myself still referring to it. For the last seven years, I have taught an upper level undergraduate/graduate level course on Bayesian Data Analysis in the physics and computer science departments at the University at Albany (SUNY). This text is required reading, and I find the students to be more than grateful for it. It is perfect for someone who wants to hit the ground running in applying these methods to real problems. This book is extremely valuable. I most highly recommend it!

A friend of mine introduced me to Bayesian analysis as a framework for handling the acoustic analysis problems which we deal with. He recommended this text as a good introduction to the theory and he is correct. I am working my way through the text and am trying to implement the exploration of the parameter spaces that must be explored. The book does not have code to help you get started, but that was not my purpose for getting the book. Sivia provides a very readable and comprehensive explanation of the Bayesian methods.

This book is well written and comprehensive. I am enjoying reading it for the first time, and plan to use it as a reference in the future. I am a professional researcher in the physical sciences.

This book is a tremendous resource. The relevant theory is presented through a series of explicit examples, in clear and concise language. The only background needed is some multivariate calculus. Highly recommended.

Awesome book on Bayesian stats. Calculus is a prerequisite to understanding it.

Solid introduction to Bayesian statistics with several examples from the physical sciences. This very well written text is self contained. The Bayesian method is motivated from first principles and basic probability. A good companion to other "classical" Bayesian statistics books such as BDA by Gelman et al.

Sivia and Skilling give a concise and clear exposition of Bayesian statistical analysis, and pair it with practical, real examples. It has been a great aid to me in doing actual data work. This text gets the balance of theoretical detail and practicality just right. In particular, abandoning the usual emphasis on analytical solutions and instead pairing real examples with numerical solution algorithms when appropriate, is perfect for someone concerned with applying Bayesian statistical analysis to real problems. A great and genuinely useful book!

I rarely write reviews on Amazon but I have to say here that of the many, many books on Bayesian theory and practice that I have read over 20 years of running a consultancy which specialises in the use of these techniques, this is certainly the best as an introduction to the modern approach to Bayesian thinking in scientific problems. After the first chapter shows why the ideas are important and where they came from, it exudes practical advice rather then unnecessary theory and continues in a carefully-considered fashion developing the complexity and background until at the end we are exposed to some pretty advanced ideas where the appropriate level of theory is then injected. Once you have absorbed the various messages thoroughly including e.g. - the caveats - how to specify realistic prior knowledge - where approximations are useful and when they are not you will be armed to use your own expert knowledge to attack problems which - although they may at first seem to be unmanageable - will be forced to yield to the subtlety and power of probability theory via Bayes' theorem if you can collect enough data of useful quality. I disagree strongly with one of the other reviewers here who likes everything except the section on Nested Sampling by John Skilling at the end. It may be a little different in tone but the technique is sound, important and rather easy to implement, and variations have been making waves in difficult high-dimensional problems in areas such as astrophysics for years now. It has a bright future and this is an excellent introduction to it. If you are interested in the modern Bayesian perspective and want real gravity, rigour and depth (along with long-winded bluster, humour and personal attacks on critics) then go for Jaynes' "Probability Theory: the Logic of Science"