Computational Statistics and Data Analysis (MVComp2)

Textbooks

I recommend that you get hold of an introductory statistics text to use during this course. There are many around, varying in their scope, level, emphasis and quality. The course does not follow a single book; below is a random sample. The course focuses on the use of statistics in the physical sciences, so some even basic recipes in the social sciences will not be covered: you may want to take this into account when getting a book. There are several texts which examine specifially the use of R in statistics, although these tend to be bit too recipe-oriented to obtain a proper level of understanding.

Barlow, Statistics
A classic. This is a well-written introduction with some useful mathematical background and simple derivations and good descriptions. It is written for physics students, so it even has a chapter titled "Errors". I can recommend it if you want to go beyond just having recipes (which you should), in particular as it contains derivations which Crawley, Everitt & Hothorn and Dalsgaard omit. Like most introductory statistics text books, it takes a very orthodox or frequentist approach (probability only appears in chapter 7!), which can make the different topics seem like set of disconnected techniques.

Crawley, Statistics. An Introduction using R
This text emphasises statistics for biological and to some extent physical (but not social) sciences. It has a reasonable balance between explaining the methods and demonstrating them in R. While there are examples, there is more of an emphasis on principles and the basic maths than there is in Everit & Hawthorn or Dalgard, for example. Indeed, the maths is very basic and many methods are not properly explained (the course will go beyond this level). However, it is visually appealing and has the advantage of being relatively cheap. Like most statistics books, it presents statistics in the traditional way (look at the Table of Contents),

Dalgaard, Introductory Statistics with R
An introduction to both R and statistics. The mathematical treatment is limited and it takes a somewhat "recipes"-like approach. As the title suggests, R takes a central role. Includes exercises and answers.

Everitt and Hothorn, A Handbook of Statistical Analyses using R
R takes quite a very central place, with lots of examples, data sets (and perhaps a few too-many screen dumps). As the title suggests, this is a guide to using R for statistics rather than a book from which you can learn statistics. Moreover, it covers several topics which are not typical for an introductory statistics course (and which we won't cover). It is as R-centric as Crawley and Dalgaard but a bit more advanced.

Gregory, Bayesian logical data analysis for the physical sciences
A good introduction to both the principles and practical application of Bayesian methods. One of very few books giving a broad introduction and guide for physical scientists (there are lots more such books for social scientists and specific analytic models). He uses Mathematica to illustrate the methods. Highly recommended.

Ivezic et al., Statistics, data mining, and machine learning in astronomy
An excellent, well-written compilation of statistical methods and machine learning methods in general, with particular attention to their application in astronomy. Lots of examples and code in python on an accompanying web site.

Jaynes, Probability theory
E.T. Jaynes was one of the main proponents of Bayesian inference. This is a a rather unconventional book describing numerous elements of Bayesian probability theory and inference, ranging from the basics through pratical examples to funadamental philosophical discussions. This book is unconventional and even polemical in places, and is probably not appropriate for a first exposure to Bayesian inference. But it contains some very thought-provoking discussions.

Lyons, Statistics for nuclear and particle physicists
The title notwithstanding, this is a useful introduction to the use of statistics on the physical sciences in general. It has some good practical advice and side notes, but is deeply orthodox in its approach to inference (the words "posterior" or "Bayes" don't even appear in the index).

Mackay, Information theory, inference and learning algorithms
Not a traditional statistics book, and perhaps not a first book for learning the very basics of Bayesian inference, but a great book for learning about inference both in principle and in practice. He has a good didactic style, and this book contains some very illuminating examples. Also look here for a good introduction to MCMC. Mackay and CUP have done us a great service by making the book available online.

Maindonald and Braun, Data Analysis and Graphics using R
This is essentially a handbook for using R for statistical data analysis rather than a book from which to learn statistics. It is similar in approach and coverage to the clasic book of Venables & Ripley (see below), in that it also covers what one would call machine learning methods (e.g. trees, discriminant analysis), but at a slightly lower level. It contains very little mathematics. At 26cm x 18cm x 3.5cm, it won't fit in your pocket.

Sivia, Data Analysis. A Bayesian Tutorial
The first edition was a great introduction to data analysis in the Bayesian perspective. (A new second edition adds three more chapters.) I recommended it if really want to understand what statistics is and how it relates to probability theory, rather than just learn a bunch of frequentist recipes. That is, don't look in here for p-values and Neyman-Pearson hypothesis testing. It includes numerous examples which are analytically solvable, but covers less on the numerical solutions. It goes beyond the scope of the course, and it does not cover R or other packages. If you only ever read one book on statistics, make it this one.

Sachs, Angewandte Statistik. Methodensammlung mit R
A very detailed and mathematical introduction to statistics. It contains a lot more than you'll need for the course but the level of mathematics is not as high (or as offputting) as first appearances might suggest. R is used to illustrate the statistics (rather than the other way around, as is the case is some other books). With problems and solutions. I've not used this book, but judging from (a) the Forward, (b) the lack of virtually any reference to Bayesian statistics or Richard Cox or Harold Jeffreys, this is an unashamedly frequentist approach to statistics. You have been warned!

Toutenburg and Heumann, Deskriptive Statistik and Induktive Statistik
This pair of books - in German - gives a detailed introduction to statistics and R from a somewhat mathematical perspective. It goes into more theory and depth than you'll need for this course. Lots of examples and solutions. I've not used it myself.

Venables and Ripley, Modern Applied Statistics with S (MASS)
"S" is a flavour of R. This books provides a very good introduction to R and its use for both basic and advanced data analysis. However, it assumes the reader is already reasonably familar with the techniques, so this is not a book which can be used alone to learn basic statistics. It goes well beyond the course, covering also topics such as GLIMs, neural networks and spatial statistics. The accompanying R package "MASS" contains many functions which will be used in the course.

Verzani, Using R for introductory statistics
Quite R-oriented and rather (too) basic. It's essentially an R guide rather than a statistics text.

(Semi-)popular books

Here is a sample of popular or semi-popular books on probability which I have read and which I can recommend to anyone interested in how probability can be used in every day life. (I don't necessarily agree with everything written in these books, but much.)

Evans, Dylan, Risk Intelligence
A study of how we (should) use simple probability theory in everyday life to help us assess risks and make decisions. Evans' thesis is that many people, regardless of intelligence, have poor risk intelligence, i.e. are not very good at assessing probability, risk, expected gains and losses. This is a very readable and insightful book.

Gigerenzer, Gerd, Reckoning with Risk
A look at how uncertainty and probability is represented and, more often, misrepresented in everyday life: in the media, in law, and especially in medicine. He guides you through interpreting probabilistic information, and how you can use this correctly to make informed decisions. He has some very interesting examples. I can also recommend his other book Risk Savvy.

Kahneman, Daniel, Thinking, fast and slow
A collection of very interesting insights - and results of experiments and surveys - into how we think about probability and statistics. He looks as how people actually assess information and make decisions. One of the main theses is that our intuitive brain is rather poor (in particular, biased) at probabilistic assessments. Very readable, and much of it is convincing.

Websites

On uncertainty, risk, bias, etc.:

• Harding Center for Risk Literacy
• Understanding Uncertainty
• Gapminder (in particular, the ignorance project)

• R software package
• An introduction to R
• The R Wiki
• R programming Wikibook
• R blog
• R things from the astrostatistics center at Penn State
• A course on R and statistics at the Statlab, University of Heidelberg