Probability and Statistics (3rd Edition)

Rating:
Summary: The best introductory manual to probabilities and statistics
Review: As a social science student (economics), statistics are crucial in a large array of topics of interest. During my studies, I have bought many probabilities and statistical manuals in order to understand the underlying theory I study (econometrics). So far, no one is better than this one (Mendelhall, Monfort among others). As someone said, probability is not an easy topic; sometimes it's pretty hard to understand particularly abstract concepts. Nevertheless, the author teaches you through an impressive quantity of examples. You don't need to be a genius in math's to understand him, because he explains pretty well. The equations are all understandable and the author's doesn't use I high level of sophistication to present complex problems. The content is pretty impressive; besides the classical probability theory (basic concepts, conditional probability, random variables, expectation...), there is an extensive section dealing with estimation techniques (maximum of likelihood, OLS, and Bayesian estimators) there is a chapter dealing with statistical tests and another with non-parametrical methods. The latter is somehow oldie and there are no explanations of the kernel density estimation or kernel regression. The other objection I can raise is that there are no explanations neither of sigma-algebras, a concept used in advanced probability. Of course, it's an introductory book, thus such drawbacks are understandable. This book should be in your library.

Rating:
Summary: Terrible book
Review: As a starter, coming from a non-mathematics background, I will recommend something else. The book goes to advanced topics pretty quickly, leaving a lot to comprehend.

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Summary: Cannot follow the logic --2nd Ed.
Review: First of all I don't know how the 3rd and 2nd Edition differ.

I am trying to learn Probability and Statistics on my own, and I find it very difficult with this book.

The book does do somethings well. It does explain concepts better than what I have read so far (Schaum's). However, in the sections on combinatorics, especially, and thereafter I cannot follow the logic. I read an example problem, the solution is given immediately with little explanation as to how. The author says the bare minimum e.g. here n=52 and k=13. I have seen the combinatoric calculations, that are the solutions, in a multitude of ways, with sums in the numerator, products in the numerator, and it is not at all obvious as to why. There is insufficient discussion in the solution.

Then in working the exercises, there is nonuniform quality with the even-number solutions. Some answers just have a number, others have the formula, and some have numbers with factorials so you can kind of guess what the author did. But in the case where there is just a number, you can't.

Can you learn from this book? Sure you can, but my prediction (after reading Ch. 1) is that it's about as difficult as trying to learn a programming language by looking at syntax and running the code, having no programming experience.

Rating:
Summary: Cannot follow the logic --2nd Ed.
Review: First of all I don't know how the 3rd and 2nd Edition differ.

I am trying to learn Probability and Statistics on my own, and I find it very difficult with this book.

The book does do somethings well. It does explain concepts better than what I have read so far (Schaum's). However, in the sections on combinatorics, especially, and thereafter I cannot follow the logic. I read an example problem, the solution is given immediately with little explanation as to how. The author says the bare minimum e.g. here n=52 and k=13. I have seen the combinatoric calculations, that are the solutions, in a multitude of ways, with sums in the numerator, products in the numerator, and it is not at all obvious as to why. There is insufficient discussion in the solution.

Then in working the exercises, there is nonuniform quality with the even-number solutions. Some answers just have a number, others have the formula, and some have numbers with factorials so you can kind of guess what the author did. But in the case where there is just a number, you can't.

Can you learn from this book? Sure you can, but my prediction (after reading Ch. 1) is that it's about as difficult as trying to learn a programming language by looking at syntax and running the code, having no programming experience.

Rating:
Summary: Intuitive and inspirative...
Review: I think this book is written in a very comprehensive way. But there may be someone who feels tired of too big kindness shown by the author. The chapter on special distributions is outstanding, especially. It is a good training to utilize basic probabilistical ideas while solving inspirative problems contained in this book, isn't it?

Rating:
Summary: best introduction to the field
Review: I used this book as a reference for my graduate level statistics course and I found it to be an excellent book to learn from. However, I have compared the first and third editions and I noticed that Prof. Schervish's additions; notably, the introduction and summary to each section, served very little; or if not, no purpose. The writing of the book is wordy enough, so these additions only made the book thicker, ...

Rating:
Summary: Great stats book
Review: I used to hate statistics, but this book is pretty clear and concise, and gets the idea across very quickly and easily. The exercise questions were of reasonable difficulty, and are put forth in a clear manner, unlike other books which present the questions in round-about manner. The examples tend to follow on or build upon from the earlier chapters, so it is best to tackle the book in the order as prescribed by the chapters.

Rating:
Summary: The best Introduction
Review: This book is very clear and readable, although its subject may be difficult. It has been a classical for a long time - first edition in 1975 - and it is extremelly well written; and, indeed, very appropriated for beginners who have taken two semester of calculus and wish to learn Statistics.

It presents all classical statistical results, formally and intuitively. The exercises have different degree of difficulty, and they are all very good - the answer, not the solution, of the even exercises are in the end of the book.

In my undergraduate, I used this book to study. So I think the undergraduate instructors on this subject should consider it a good option to be adopted as a textbook.

Rating:
Summary: Good intro for self-study
Review: This is an introductory book. It also fits in introductory level of Mathematical Statistics. The prerequisites are introductory calculus and linear algebra. Most theorems are proved in calculus style but there are some gIt can be shownsh that are not proved. So some readers may not be satisfied with the book, especially Math majors.

Logical steps are shown in detail; else logical gaps are contained within a level such that a first time reader can fill in the gap with a pencil and paper. Occasional mix with Bayesian perspective is also a feature. Answers to odd-numbered exercises are provided except ones that ask derivations and proofs. Exercises that require some tricks are provided with hints. In these respects, this textbook is suitable for self-study.

Upon completion of the entire material, I feel concepts are developed well up to Hypothesis testing Chapter 8 where the presentation of material reaches climax and its level of exposition is somewhat higher than other chapters. Thereafter, simple linear regression is treated in detail, but coverage and detail of materials seem to deteriorate from the following general regression section, nonparametrics and thereafter. Kolmogorov-Smirnov Tests section is treated nicely though. Anova section lacks in coverage. The new simulation chapter is presented more like a demonstration rather than an introduction.

I have never seen the previous 2nd edition (unfortunately Dr. Degroot is no longer with us), but according to the preface of this 3rd edition, Dr. Schervish describes 8 major changes from the previous edition. Notable are some material removed from the previous (likelihood principle, Gauss-Markov theorem, and stepwise regression), some added (lognormal distribution, quantiles, prediction and prediction intervals, improper priors, Bayes test, power functions, M-estimators, residual plots in linear models and Bayesian analysis of simple linear regression), more exercises and examples, special notes, introduction and summary to each section, and so on. I find the last in the list is somewhat disturbing, especially introduction parts that are often redundant with the very next paragraph. On the other hand, I find that special notes provide good insights.

I wish they included introduction to Statistical Decision theory, full coverage of regression analysis to be usable such as diagnosis, transformation and variable selection, coverage of Multivariate Normal distribution, more coverage and depth in nonparametrics and simulation, and lists of recommended readings for further study at the end of each section with comments.

There are a noticeable number of typos as of this first printing I have. I sent suggestions for typos and was impressed that Dr. Schervish updated errata list within a few days at his homepage. I wish all authors were like him being responsible.

Rating:
Summary: How to remain a classic
Review: This new editon mantains the features that have made it a classical for a long time:

- Clearly written;
- Tough subjects are made understandable even for beginners;
- Classical results are presented rigorously after a bunch of examples;
- Many exercises, well posed, whose solutions are found in the end of the book (just even exercises).

This books has been long without a revision and we can see easily that it is much better. The main improvement is the computational treatment of Statistics in terms of theory and exercises. And, of course, it is visually more pleasant.

You may think this is little, though. But, a classical is so well done that there is not much more to do. This is the case. So the second author adds what was difficult when DeGroot first wrote it (computational stuff, as I said) and suppress what is out of fashion or has been overcome.

I think it is still the best option to start out to learn Statistics.