Mary C. Meyer
SIAM 2019, 707 PAGES
PRICE (HARDBACK) £104.00 ISBN 978-1-61197-577-2
This book covers most of the statistical methods which are in wide use by the scientific community. The approach is very practical, emphasising the application of the theory to real world problems. Consequently, there are a large number of exercises taken from real world situations with solutions to half of them in an appendix of 160 pages. Having said that, the theory is fully explained with rigorous proofs of theorems given in detail for those who are prepared to go through them.
Some purists may criticise the treatment of probability theory as there is no mention of measure theory or Borel sets for example. However, the book is focussed on the application of probability and statistical theory to real world problems and is directed towards those involved in postgraduate research in the applied sciences rather than the pure mathematician.
I have to say, when I first studied statistics as an undergraduate (not from this book of course), I found it very boring. Just a lot of tedious numerical procedures which led to some imprecise conclusions. Later when my work required me to carry out analysis using some of the techniques described in this book, I realised how powerful, and indeed, beautiful the subject is. Although probability theory and statistics is all about uncertainties and incomplete data, it still amazes and delights me that we can use this uncertain and incomplete data to make very precise and definitive statements using the methods described in this book.
The book is refreshing in its layout, consisting of sixty very short chapters, each covering a specific topic in the theory. Each chapter explains the theory, in just a few pages, and is followed by a summary of the topic and a large number of exercises. Many of the chapters can be read independently, making it ideal for the student or researcher who needs a particular method to analyse their specific kind of data sets.
The R programming language is used throughout to perform calculations and produce graphs. The title of the book includes the word ‘practice’ which is very pertinent. This is not a book to use in order to learn the R language, but it does give many code snippets in R. Someone with only a grounding in the R language would benefit from using these code snippets while a more experienced R programmer may well be glad of the practice. In fact, anyone familiar with programming in a modern language like C, MATLAB, or Python should be able to learn R without too much difficulty, especially when there are a number of graphical user interfaces like RStudio available, for example.
The huge number of exercises and problems from a wide range of disciplines including engineering, astronomy, and sociology means that researchers and students will almost certainly find examples of the way the theory can be applied to their particular area of study.
Considered as a catalogue of statistical methods the book is instructive and would be a valuable resource for those working in applied science who need to analyse data sets of different types.
Trevor Bailey CMath FIMA
Book review first published in Mathematics Today August 2021
