Comment by gaur | Hacker News Reader

Comment by gaur | Hacker News Reader

Who is this book supposed to be for? Given the heavy emphasis on formalism (theorem, proof, theorem, proof, theorem, proof), and the lack of a single example that actually computes a number, I hazard a guess that this book is not for people who actually want to apply statistics to real problems.

A while back I had to teach myself Fisher matrices and the Cramér–Rao bound to solve a problem I was working on. I quickly found that 90% of statistics textbooks and lecture notes on this subject are completely useless for people like me who want to arrive at a number, not some abstract expression involving angle brackets or measures or E[...] or whatever.

The Wikipedia article on Fisher information [0] is one such example of a resource that is full of useless formal crap that crowds out an explanation for real people about how to use this statistical tool. This book appears to be of the same ilk. (Also, this book apparently does not discuss the Cramér–Rao bound. Ironic given the book's title.)

If anyone is curious, the single best explanation of the Fisher matrix and the Cramér–Rao bound that I have found is tucked away in an appendix of the Report of the Dark Energy Task Force [1]. In one page they manage to concisely and clearly explain where the Fisher matrix comes from, how to compute it, and how to apply the Cramér–Rao bound.

[0] https://en.wikipedia.org/wiki/Fisher_information

[1] http://arxiv.org/abs/astro-ph/0609591

I found this book to be a godsend. I never took statistics and always wanted to better understand the deep conceptual ideas in the field. I had so many frustrating experiences with books that came highly recommend to me, and turned out to be not what I wanted at all. They spend chapters and chapters beating around the bush, conversationally talking about general ideas around data management and measurement bias and research design and different ways of charting data sets.

I cannot tell you how frustrating this was for me. I wanted just the meat: the core mathematical concepts on which statistical models and inferences are built. Don't tell me a folksy story about gathering soil samples, show me the tools and what they can do, both their power and their limitations. I can think for myself about how to apply those concepts.

I loved this book for being exceptionally clear and terse. I was hooked from the first sentence: "Probability is a mathematical language for quantifying uncertainty." That one sentence makes the concept clear in a way that the entire chapter on probability from "Statistics in a Nutshell" (http://www.amazon.com/Statistics-Nutshell-Sarah-Boslaugh/dp/...) did not.

I'm not someone who thrives on theorems and proofs, I thrive on concepts. And I found this book dense with clear explanations of the key concepts.

>Who is this book supposed to be for?

I don't have the book here at work so I can't quote the book's introduction, but in some sense the title is meant to be literal. It's an attempt to cram an entire 4-year undergraduate statistics program into a single book, and in my opinion it's mostly successful. This book is is my go-to reference for those "Ahhhh, I remember hearing about [insert statistical test here] back in college, what was it again?" moments.

When I was taking a class in Statistical Inference, we used a combination of Statistical Inference (Casella and Berger), Introduction to Mathematical Statistics (Hogg and Craig) and Probability and Statistics (Degroot and Schervish). If you're still interested in learning about Fisher Information and the Cramer-Rao Lower Bound, you can refer to pages 514 - 521 of Probability and Statistics 8th Ed. It has a number of proofs which you can skip if you're not interested but it also provides a number of examples using different distributions to calculate both the Fisher Information and the Cramer-Rao Lower Bound.

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