This volume is an introduction to probability and statistics for experimental physical scientists - for those physical scientists whose success depends on the wise use of experimental data. Statistics is the study of efficient methods for the collection and analysis of data in a framework that explicitly recognizes and allows for the reality of variation or randomness. Probability is the branch of mathematics that provides tools for the description of randomness; it is thus essential background for the enterprise of statistics, and is basic to the understanding of nondeterministic phenomena.
As the phenomena studied by physical scientists become more complex, statistics and probability become more important to progress in the physical sciences. Larger sets of increasingly complex and noisy data are needed to help answer basic scientific questions. In this book we provide a "source of first resort" for physical scientists who need probabilistic and statistical tools in their research. Physical scientists can and do develop statistical tools of their own, but given an appropriate entry into the statistical literature such as this volume, their work will be easier, more efficient, and more productive. They will be ably to quickly find out what is already available (and in the process avoid pitfall encountered by others) and will be able to make use of the best existing statistical technology.
This volume is not a text on mathematical theory, although a level of mathematical sophistication commensurate with graduate training in the physical sciences is assumed. Instead, it is a readable, self-contained introduction to a variety of methods (old and new) that seem to us most widely applicable and important in the physical sciences. Authors have illustrated their discussions with real physical sciences and also data sets. In all of the chapters, the authors have supplied helpful bibliographies for further reading for those who need to learn more than can be presented in a single volume like this.
In recruiting authors for this book, we (a physicist and a statistician) looked for a creative mix of statistically literate physical scientists and for statisticians with a real interest in the physical sciences. Therefore, the volume reflects a broad understanding of the real modeling and data analysis needs of the modern physical sciences, and also the best existing probabilistic and statistical methodology. As editors, our hope is that it will serve as a catalyst for interaction between physical scientists and statisticians, reaching far beyond the particular effort that produced it. In the book, physical scientists will find both tools to support their research and evidence that statisticians are interested in crafting such tools. Statisticians will find fascinating problems of genuine scientific importance, easily adequate to occupy their "tool-making" and collaboration efforts full time.
The structure of this book is as follows. It consists of four rather distinct sections. Chapters 1 through 5 provide an introduction to probability modeling for the physical sciences, including discussions of time series and spatial models, and an introduction to Monte Carlo (probabilistic simulation) methods. The second section consists of chapters 6 through 9, which provide the basics of probability-based statistical inference, including discussions of goodness of fit and maximum likelihood methods and inferences from least squares analysis. Chapters 10 through 13 discuss the important topics of statistical from time series and spatial data. The last section, consisting of Chapters 14 through 17, discusses some specialized (but nevertheless important) topics, most of which are only recently available for application through advances in scientific computing. In addition to Bayesian methods, this section contains discussions of applications of Monte Carlo methods to both particle and atmospheric physics and a chapter discussing the capabilities of modern statistical computing systems.
We expect that most physical science readers will use this volume a chapter at a time as they need particular types of statistical methods. Nevertheless, as readers examine Chapters 6 through 17 for data analysis methods, we also expect that they will spend time in Chapters 1 through 5 familiarizing themselves with the modeling background that supports and motivates the statistical methods discussed in the last 12 chapters.
As we come to the end of our work in this volume, we thank the chapter authors for their excellent cooperation in bringing this book together. They have not only written several drafts of their own chapters (reacting with good humor to editorial meddling), but also provided extremely helpful reviews of others' drafts and kept to the ambitious schedule that we set when recruiting them. It has been a pleasure to work with them on this project, and we believe that the reader will find their contributions both engaging and illuminating.