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"

Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1

which is the 'reference book' (though untypical in form & slightly unfinished) to support this excellent practical introduction.

Good introductory book an Bayesian statistics.

Concise and quite complete, requires some background in calculus but very accessible book.

A solid introduction but, as a statistician by trade, I detected more than a little bias towards the "Bayesian is great, everything else sucks" which plagues this type of text. An early dismissal of the concept of randomness without any real discussion was also particularly frustrating. The content is good but the writer comes across as more than a little arrogant. It does an excellent job mathematically and includes some C code (not something I'm familiar with so I can't comment on it's usefulness). There are also plenty of examples to illustrate the theory which is always nice.

Next time I would look for something a little more friendly, but the factual content is good.

One of the best books in practical application of Bayesian statistics. It has clear examples and solutions applied.

A must have book for the professional statistician who wants to aquire more knowledge about challenging aspects of the Bayesian inferences.

One of my favourites. Well written, good book.

This is a _great_ book. The early chapters which introduce the broad concepts underlying Bayesian reasoning are particularly strong. Although it's aimed at students of physics, it would be useful to a much broader range of disciplines (I'm a psychiatrist which is about as far from physics as you can get...).

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

Great book, actually. It came in perfect condition. (:

Easily accessible step by step walkthrough of Bayesian data analysis and associated techniques and a good introductory resource that formalizes a lot of knowledge that may be imprecisely assumed. Every STEM graduate student could benefit by going through this in their spare time to elevate the quality of their data analysis.

Beware: this high-quality text puts considerable demands on the reader's ability to comprehend and use mathematics. On the other hand, this is exactly what the text is for.

Numerous, excellent examples; almost all calculations are presented, so the reader can find a step if he/she missed one. Hence: a tutorial.

Highly recommended.

Muy buena compra

This is a truly excellent text; it differentiates clearly between conventional statistical and probabilistic methods, and those unique to the Bayesian tradition(s). It provides clear examples, and walks the reader through procedures that might otherwise be most opaque. The authors' intentions are clearly to expound a tradition of academic and scientific excellence, rather than simply to produce a textbook for graduate students to work from.

Possible cons: This material is not easy to pick up. The authors make it as lucid as I, as a self-motivated student and researcher, can imagine it being in a text, but it is simply not easy material to work with. That being the case, one potential objection might be that in some cases the reader may not understand WHY a particular technique is important to use in the manner it is being described without significant reflection.

Cons aside: I recommend this book very highly to any serious student of probability and/or statistics, and to any mathematician or computer scientist who wants to expand her/his horizons and capabilities. It is possible that an advanced student of Bayesian methods might find most of the material in the book familiar, but it is unlikely that she/he will have learned ALL of it, or have a reference book readily available that is so clear about every topic included as this one. It is also uniquely affordable, for such a significant purchase.