W. John Braun

Data Analysis and Graphics Using R: An Example-Based Approach

Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides. The emphasis is on hands-on analysis, graphical display, and interpretation of data. The many worked examples, from real-world research, are accompanied by commentary on what is done and why. The companion website has code and datasets, allowing readers to reproduce all analyses, along with solutions to selected exercises and updates. Assuming basic statistical knowledge and some experience with data analysis (but not R), the book is ideal for research scientists, final-year undergraduate or graduate-level students of applied statistics, and practicing statisticians. It is both for learning and for reference. This third edition expands upon topics such as Bayesian inference for regression, errors in variables, generalized linear mixed models, and random forests.

Forest Fire Risk Assessment: An Illustrative Example from Ontario, Canada

This paper presents an analysis of ignition and burn risk due to wildfire in a region of Ontario, Canada using a methodology which is applicable to the entire boreal forest region. A generalized additive model was employed to obtain ignition risk probabilities and a burn probability map using only historic ignition and fire area data. Constructing fire shapes according to an accurate physical model for fire spread, using a fuel map and realistic weather scenarios is possible with the Prometheus fire growth simulation model. Thus, we applied the Burn-P3 implementation of Prometheus to construct a more accurate burn probability map. The fuel map for the study region was verified and corrected. Burn-P3 simulations were run under the settings (related to weather) recommended in the software documentation and were found to be fairly robust to errors in the fuel map, but simulated fire sizes were substantially larger than those observed in the historic record. By adjusting the input parameters to reflect suppression effects, we obtained a model which gives more appropriate fire sizes. The resulting burn probability map suggests that risk of fire in the study area is much lower than what is predicted by Burn-P3 under its recommended settings.

A First Course in Statistical Programming with R: Programming with R

Programming involves writing relatively complex systems of instructions. There are two broad styles of programming: the imperative style (used in R, for example) involves stringing together instructions telling the computer what to do. The declarative style (used in HTML in web pages, for example) involves writing a description of the end result, without giving the details about how to get there. Within each of these broad styles, there are many subdivisions, and a given program may involve aspects of several of them. For example, R programs may be procedural (describing what steps to take to achieve a task), modular (broken up into self-contained packages), object-oriented (organized to describe operations on complex objects), and/or functional (organized as a collection of functions which do specific calculations without having external side-effects), among other possibilities. In this book we will concentrate on the procedural aspects of programming. As described in Chapter 1, R statements mainly consist of expressions to be evaluated. Most programs are very repetitive, but the amount of repetition depends on the input. In this chapter we start by describing several flow control statements that control how many times statements are repeated. The remainder of the chapter gives advice on how to design and debug programs. Flow control The for() loop One of the goals of this book is to introduce stochastic simulation. Simulations are often very repetitive: we want to see patterns of behaviour, not just a single instance. The for() statement allows one to specify that a certain operation should be repeated a fixed number of times. Syntax for (name in vector) { commands } This sets a variable called name equal to each of the elements of vector, in sequence. For each value, whatever commands are listed within the curly braces will be performed. The curly braces serve to group the commands so that they are treated by R as a single command. If there is only one command to execute, the braces are not needed.

Parametric modeling of reaction time experiment data.

A simple parametric model is proposed for data from a point-process version of a reaction time experiment. It is used to statistically check for the presence and nature of nonlinear inhibition in the eye-brain-hand system, as well as to study the nature of the reaction time delay distribution. The model tells us that, in principle, the second-order intensity estimate can be used to determine whether the experimental subject is systematically observing the first or the second of two flashes transmitted in short succession. Nonparametric estimates of second-order intensity functions are used in conjunction with this model. In particular, the model allows for the computation of good bandwidths for intensity curve estimation. A parametric bootstrap can also be implemented. Our methods are illustrated with 12 runs of data from a real reaction time experiment. It is found that nonlinear inhibition is present in the eye-brain-hand system. However, there are insufficient data to distinguish between log-normality and normality in the reaction time distribution, due partly to confounding with the particular kind of nonlinear inhibition present in the system.

One Sided Tolerance Limits Via Smoothing

Abstract A nonparametric method for computing tolerance limits in small to moderate non-normal samples is proposed. The method is based on confidence intervals for quantiles. The quantiles are first estimated using a kernel quantile estimator which is known to have an asymptotic normal distribution. Approximate confidence intervals can be easily constructed using this normal approximation. The proposed kernel quantile limits are compared by simulation with the classical normal tolerance limits as well as some tolerance limits that are known to have excellent behaviour in large samples. The simulation results indicate that the kernel quantile limits can be somewhat conservative, but they are often much more accurate than the other two methods.

Review of weighing the odds, by D. Williams

Weighing the Odds, by David Williams, is published by Cambridge University Press (publishing date 2001, ISBN 0-521-00618-X). 556 pp. £ 24.95 The authors motivation in writing this book might be inferred from a statement made at the end of the eighth chapter: that I have not been more actively involved in Statistics throughout my career and my wish to persuade others not to follow my example in that regard. Weighing the Odds is a book on Probabili ty and Statistics, written from the perspective of a probabilist. Its intended audience is mathematics students who have not yet been exposed to these subjects. The authors objective is to entice these students by introducing the more mathematical elements of the subjects. The book is highly idiosyncratic, and the writers personal views are never far from the surface. Thus, the book is perhaps the most lively account of these two subjects that we are aware of. The book contains a relatively small, but interesting treatment of traditional problems and some newer-looking problems. Some excellent hints are provided for some of the more challenging problems. A lot of statistics (all?) is based on conditioning. We cannot write down a model or compute a probability without conditioning on something. At the same time, conditioning is often one of the beginning students greatest difficulties with the subject of probability and statistics. Therefore, it is refreshing to see a book which opens by addressing conditioning so boldly with an attempt at an intuitive look. Many of the examples are very good: the Monty Hall problem (referred to as the Car and Goats Problem) , the Two Envelopes problem, and the Birthday problem are all described clearly, and analyzed carefully either in Chapter 1 or later on in the book. The example referencing system seems confusing, at first. The author warns that the preface should be read first; this warning should be heeded if for no other reason than to discover that problem 19A is really problem A on page 19. Chapter Two contains, among other things, a collection of measure-theoretic results. Were scratching our heads a bit, wondering why the author seems so insistent on avoiding measure theory, when he has gone almost halfway there. Some of the results, such as the monotone convergence theorem, are useful as Facts , but the description of the n system lemma seems to be deficient. We are not sure anyone without a background in measure theory already would really know what the author is talking about. Similarly, the Banach-Tarski paradox may be bewildering to many readers. On the plus side, we think that the hat-matching problem is a good nontrivial application of the inclusionexclusion principle. Chapter Three gives a concise discussion of random variables, density functions, mass functions, and expectation, and Chapter Four begins with a discussion of conditional probability and independence before moving into the laws of large numbers. The author claims that the proof of the Kolmogorov strong law is much too difficult to give. We are a bit perplexed about this, since all of the ingredients are given, and that the proof really is not that much difficult than, say the proof of Stirlings formula (admittedly as optional, but on page 13!). The inclusion of the Bernstein polynomial proof of the Weierstrass approximation theorem is a nice idea. The only real look at Markov chains occurs in the section on random walks. The reflection principle is described briefly. The section the strong Markov property is rightly indicated as optional reading. The treatment of simulation is excellent. It is unusual for pseudorandom number generation to feature in a text on probability, but it fits into the context naturally. The presentation is careful, and it is nice to see the Wichman and Hill (1982) pseudorandom number generator featured.