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All of Statistics: A Concise Course in Statistical Inference

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Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. 
The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data. 

462 pages, Hardcover

First published December 4, 2003

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About the author

Larry Wasserman

4 books8 followers
Larry A. Wasserman is a Canadian statistician and a professor in the Department of Statistics and the Machine Learning Department at Carnegie Mellon University.

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Displaying 1 - 27 of 27 reviews
Profile Image for Michiel.
344 reviews63 followers
April 23, 2014
Very good reference on notions on probability, statistics and machine learning. Not ideal to learn the matter from scratch, but ideal to refresh and supplement your knowledge when you do a PhD.
Profile Image for Hamish.
403 reviews23 followers
August 22, 2021

- The core problem in probability is "given a generating process, what does the output look like?"
- The core problem in statistics is "given some output, what does the generating process look like?"
- If A and B are disjoint events with non-zero probability, then they cannot be independent (because P(AB)=0, but P(A),P(B)>0). "Except in this special case, there is no way to judge independence by looking at the sets in a Venn diagram."
- Mistaking P(A|B) for P(B|A) is called the prosecutor's fallacy.
- The rule that "P(B) = sum_i P(B|A_i) if {A_i} is a partition" is called the Law of Total Probability.
- I don't understand this: you can't generally assign probabilities to all subsets in a sample space, so attention is restricted to sigma-fields.
- A geometric distribution is of the form P(X=k)=p(1-p)^{k-1}. Why is this called geometric? Because it's a geometric sequence (see here for more details).
- The rate of the sum of two Poisson distributions is the sum of the rates. That is, if X1 ~ Poisson(n,lambda1), and X2 ~ Poisson(n,lambda2), then X1+x2 ~ Poisson(n,lambda1+lambda2).
- The mathematical construction of a random variable is a mapping from sample space Omega to R. Just like in computers.
- Standard normal distribution is denoted Z, with pdf and cdf denoted phi(z) and Phi(z).
- There is no closed form of Phi(z).
- If Xi ~ N(mi, si^2), then sum Xi ~ N(sum mi, sum si^2)
- The logic of the gamma distribution, cauchy, and X^2 distributions continue to elude me.
- Cauchy distribution is like Gaussian, but with thicker tails. It's a special case of t-distribution.
- The multinomial distributions has binomial distributions as marginal distributions.
- How to find the pdf of a transformation x -> y of a random variable: 1) find the pre-image for each y, 2) evaluate the CDF of the pre-image, 3) differentiate the CDF to get the PDF.
Profile Image for Terran M.
78 reviews91 followers
May 8, 2020
From the title, one expects this book to be comprehensive and encyclopedic, but I found the opposite to be the case. This is a very mathematical rapid-survey of statistics which does not explain how to actually do any of the things that a working engineer or scientist would need to do.

I think the audience of this book is "mathematicians who find books with more equations than text to be comfortable and easy to learn from, who also know nothing about statistics and want a quick survey of the field, and who will use statistics to prove theorems and write papers instead of actually calculating anything." This book is completely unsuitable for engineers; for those I would recommend Baclawski and then Diez. Even Casella&Berger is much more accessible than this book.
Profile Image for Zach.
189 reviews
May 30, 2022
This could possibly be useful as a reference book. Otherwise, it's math without any explanations, unless you find symbol manipulation explanatory. I'm not afraid of math (I minored in it and have a degree in CS), but I don't understand a formula without first understanding the concepts behind it. I expect this is true of most people. It is pretty funny to me that this book is billed as 'for people who want to learn probability and statistics quickly... No previous knowledge of probability and statistics is required.'
Profile Image for Chris.
142 reviews28 followers
December 31, 2018
Doesn't actually do what it says, but makes headway toward that goal.

If you want to learn about the chi-square, don't read Wikipedia. Read Wasserman.
22 reviews
August 1, 2018
I learnt Statistics for 2 - 3 times in campus, but I still find this book is too hard, not suitable for beginner, some of the symbols in the theorem come from nowhere, and some of the definition needs further explanation. I can understand until chapter 7, but the symbols already beyond I can remember or understand.
9 reviews8 followers
September 30, 2020
It was my first statistics book and I disliked the book since the author does a poor job explaining the details. If you are new to statistics without a lot of training in mathematics ANY other book would be better than this book.
64 reviews2 followers
March 4, 2021
Great exercises, pretty comprehensive treatment and very readable without being slow-paced.
58 reviews1 follower
April 25, 2021
A good refresh on the probability/statistics topics.
Profile Image for 原輔 曹.
1 review
June 16, 2022
It is my textbook for my statistics course. I think it is a good choice for somebody who has learned probability.
6 reviews
December 30, 2022
I think it is a very solid and powerful reference for anyone who wants to take a comprehensive view of the statistical science approach.
Profile Image for afloatingpoint.
132 reviews25 followers
April 19, 2016
10/15/2015: So far, this is a really good book with comprehensive material, simple examples, rich problems, and most importantly easy to understand.

12/8/2015: I like everything about this book, except the title. It may receive some complaints about not discussing in depth some topics, but one can always go look up and read more on their topics of interest. Nonetheless, this is a very well written book!
115 reviews15 followers
March 20, 2021
The author states that he wrote the book to help get engineering students up to speed. The topics and depth are in line with what one would expect from a mathematical statistics book. It's a good book for finding out what is out there, but most discussions are too brief for most people to learn the material from this book.
Profile Image for David.
10 reviews4 followers
August 14, 2007
The material covered in this book is not covered in sufficient depth to understand it unless you have covered once already. That said this book is a great reference: collections of useful theorems and properties.
59 reviews
January 20, 2021
A VERY difficult read and took some time for me to refresh my rusted knowledge of statistics.

My first pass was a browse through this. I look forward to many months of banging my head against this book.

I wish it came with an answer key but apparently, that costs extra.
49 reviews9 followers
March 5, 2013
A bit harsh for an introduction, requires mathematical maturity. Great reference though.
Displaying 1 - 27 of 27 reviews

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