Devinderjit Sivia and John Skilling
reviewed by Matúš Medo
posted by Matúš Medo
Courses on probability and statistics leave many students with the unpleasant impression that statistics is a messy collection of ideas and recipes, often without strict adherence to the rules of logic and common sense. Authors had similar feelings many years ago but, as the story often goes, their initial doubts turned into deep understanding and the ability to clearly express their thoughts. Their slim book gives a concise and readable (yet rigorous) exposition of Bayesian methods in data analysis.
The first half of the book (dubbed as 'The essentials') is accessible to undergraduate students but some preliminary knowledge of statistics is suitable nevertheless. Consistently based on the logical scheme prior information + data -> posterior information, the reader is gradually guided through parameter estimation, model selection, and the principle of maximum entropy. Interestingly, while the examples used to illustrate the theoretical concepts are rather simple, most of them allow the authors to highlight some peculiar behavior.
In the second half (dubbed as 'Advanced topics'), authors deal with more complicated problems, some of which are still subjects of ongoing research. Emphasis shifts from theoretical concepts, such as non-parametric estimation and dealing with outliers in least-squares estimation, to numerical techniques, nested sampling in particular.
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