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Probabilistic Forecasting and Bayesian Data Assimilation

Sebastian Reich and Colin Cotter
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Peter Rabinovitch
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I am very fortunate that Brian Borchers very recently wrote an excellent review of a similar book on the same topic, and provided a terrific explanation of what, exactly, data assimilation is. So go and read his review first.

Now on to the review of this book. I very much liked the writing style, as the book is full of examples and explanations. That being said, the authors take more of an engineering approach than a mathematical approach, so there are few proofs.

After the prologue, the first section contains four chapters on the basics of probability and statistics. If you’ve done any graduate level work in the field, this will be almost all review, although some of the terminology is a little different, so skim it quickly. Then there is a second section of four chapters, the meat of the book, on Bayesian data assimilation. The material is very interesting. I think fleshing out the details in full rigor could make for a very interesting masters project or course.

The only real negative comment I have about the book is that the code samples are in Matlab, which is not free. I’d much prefer that code samples in books were done with software that anybody can obtain regardless of budget. The code samples might work with Octave (a free clone of Matlab), but I did not have the time to try them out yet.

Peter Rabinovitch is a Senior Performance Engineer at Akamai, and as been doing data science since long before “data science” was a thing. He has experienced compatibility issues between Matlab and Octave code in the past and these days prefers to work in R.

1. Prologue: how to produce forecasts
Part I. Quantifying Uncertainty:
2. Introduction to probability
3. Computational statistics
4. Stochastic processes
5. Bayesian inference
Part II. Bayesian Data Assimilation:
6. Basic data assimilation algorithms
7. McKean approach to data assimilation
8. Data assimilation for spatio-temporal processes
9. Dealing with imperfect models