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All of Statistics: A Concise Course in Statistical Inference
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.
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
About the author
Larry Wasserman
4 books8 followersLarry 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
January 30, 2021
Really good reference. Its probability and inference parts are awesome.
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.
August 22, 2021
I DID IT! I FINISHED IT! I'M FREE!
Notes:
- 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.
Notes:
- 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.
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.
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.
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.'
August 4, 2018
Not a good one for getting started, very formal and less intuitive.
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.
If you want to learn about the chi-square, don't read Wikipedia. Read Wasserman.
May 14, 2019
The perfect statistics book for me... ❤️
I now feel better equipped to read more stats books...
I now feel better equipped to read more stats books...
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.
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.
March 4, 2021
Great exercises, pretty comprehensive treatment and very readable without being slow-paced.
April 25, 2021
A good refresh on the probability/statistics topics.
February 17, 2022
Excellent book... short and concise.
June 16, 2022
It is my textbook for my statistics course. I think it is a good choice for somebody who has learned probability.
July 4, 2022
Wanting to re-read again >
Notes in progress
Draft
Notes in progress
Draft
December 16, 2022
Nice reference book. Just as reference. Don't try to self-study from it.
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.
March 2, 2021
A concise reference book for frequentist statistical practice up until the late 1990s or so.
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!
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!
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.
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.
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.
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.
August 8, 2007
Great if you like statistics, painful if you don't...
March 5, 2013
A bit harsh for an introduction, requires mathematical maturity. Great reference though.
August 30, 2016
A must have
February 10, 2014
Useful.
September 11, 2012
Very nice book. Some concepts have been explained with great clarity.
Displaying 1 - 27 of 27 reviews