# Handbook of Probability: Theory and Applications

Handbooks

### Tamás Rudas

• Chapters
• Front Matter
• Back Matter
• Subject Index

## Preface

There exists no scientific knowledge without some degree of uncertainty concerning its validity, reliability, or precision. Probability is our most important construct to deal with this uncertainty. Although uncertainty exists in all fields of scientific activity, the standard of dealing with it varies from subject to subject, depending mostly on the particular way in which scientific knowledge is obtained and formulated, but also on traditions. This Handbook sets the ambitious goal of presenting the fundamentals and several applications of probabilistic thinking in the social and behavioral sciences, economics, and law. Elements of probability are included in most relevant university curricula, but very often probability is discussed as background material for statistics only, generating the impression that statistics itself is nothing else than the application of existing statistical methods. Just like the role of careful statistical modeling, as opposed to routine application of statistical tools, is often suppressed, the presentation of probabilistic thinking is also often reduced to the static presentation of simple rules of the calculus of probability.

In fact, probability is a lively subject that develops very fast, and some understanding of it is necessary for the correct interpretation of any scientific finding. The chapters of the Handbook cover different aspects of probability. Some are philosophical, some are mathematical, and some are statistical in their nature. The diversity of the approaches to probabilistic thinking is well represented by the diverging views of what is probability and how it is related to reality. The authors of Chapters 2 and 3 agree that probability is a construction that helps us conceptualize uncertainty, but Chapter 2 takes the view that observable events occur with a certain probability that may be revealed by repeated observations (the so-called frequentist definition of probability), while Chapter 3 discusses probability related to subjective judgment and expectation (the so-called subjective probability). On the other hand, Chapter 4 illustrates that not all subjective interpretations of probability are consistent. Closely related to probability is the concept of randomness: An event is random if the observer has uncertainty with respect to it. The observer may choose a deterministic or a stochastic model to describe the behavior of the possible observations, and the choice is often dictated by the available knowledge and other resources, but very often it also has an element of free choice (Chapter 2). On the other hand, Chapter 9 attributes “real” randomness to certain physical processes and takes the perhaps surprising but very useful position that processes that cannot be distinguished from a real random process with a reasonable amount of effort may be considered random. Furthermore, Chapter 6 distinguishes between aleatory and epistemic uncertainty (to refer to a kind of impossibility to remove uncertainty and to the actual lack of knowledge to do so). These issues are also related to the debate between the frequentist and the Bayesian views on statistical analysis (discussed in Chapters 5 and 6). Yet another possibility of handling uncertainty by using fuzzy sets is mentioned (in a particular context) in Chapter 20. A related topic that has attracted significant scientific interest recently and is taken up in more than one chapter is the definition and analysis of causality in stochastic models—that is, when causal relationships have to be identified in the presence of uncertainty. Chapters 8 and 23 discuss the most important approaches, one through the definition of individual causal effects and the other by the application of graphical models. There are several other topics discussed in more than one chapter, including time-dependent observations, measurement of and protection from investment risk, and DNA evidence.

While some of the chapters cover standard textbook material in a concise way and some others tend to describe cutting-edge developments, the presentation is intuitive throughout and the mathematical details are suppressed, so that all chapters are accessible with good high school or first-year college mathematics. The Handbook largely neglects the calculus of probability: Such details are left to specialized textbooks, and it concentrates mostly on the conceptual development of probabilistic thinking and on many of its applications. Most of the chapters are self-contained, which implies that some material is discussed in more than one chapter, perhaps from a different perspective, as was illustrated above. The references given at the end of each chapter vary from mentioning the few most fundamental sources to listing a complete collection of research papers, depending on the material covered in the chapter.

The Handbook is divided into three parts. The first part covers the theory of probability and gives an introduction to its mathematical and philosophical aspects in a fairly nontechnical way but well beyond the level at which most social or behavioral scientists study this topic at university. Chapter 1, written by Peter Lee, presents the most important developments in the history of probability theory. Many of these results are discussed and explained in detail in later chapters. Chapter 2, written by Herwig Friedl and Siegfried Hörmann, summarizes the main results of probability theory, as a mathematical subject. They give an intuitive but precise description of some of the more involved theorems, including the law of large numbers and the central limit theorem. Chapter 3, written by Igor Kopylov, gives an overview of the subjective definition and interpretation of probability. The chapter shows that many of the fundamental properties of probability, which were derived in the previous chapter in a frequentist setting (as this leads most easily to these results), may also be obtained from a different approach to the relationship between reality and probabilistic thinking. Chapter 4, written by Nicholas Shackel, takes a critical view on assumptions and beliefs often associated with probability and shows many of these to be untenable. These paradoxes occur, of course, not within the mathematical theory of probability but rather in our thinking when we try to formulate probabilistic models to describe reality.

The second part extends the theory given in the first part and discusses the general ways in which probabilistic approaches are used in research. The coverage here concentrates on applied probability and theoretical statistics. Chapter 5 is an account of the standard (frequentist) way in which probability theory is applied in statistics. Probability theory tells us how random observations from a population (“the reality”) tend to behave, depending on the characteristics of this population and the sampling procedure, and statistics uses this knowledge to infer from observations to the characteristics of the population whence they were selected. Chapter 6, written by Tony O'Hagan, gives an account of Bayesian statistics and compares it with the frequentist approach. The main difference is that in frequentist statistics the characteristics of the population from which the observations came are assumed to be fixed but unknown, while in Bayesian statistics uncertainty regarding population characteristics is allowed (and is described probabilistically). However modest this difference appears to be, it leads to wide-ranging deviations in terms of the questions that may be asked and also in the ways in which those questions are answered. Chapter 7, written by Mauro Gasparini and Maria Piera Rogantin, describes experiments—one of the most important ways in which researchers collect information with respect to reality. The design of experiments is fundamental in technical applications of statistical analysis, but the chapter, in addition to defining the general concepts of main effect and interaction, emphasizes conceptual aspects and applicability to human populations. Chapter 8, written by Michael Sobel, gives an account of one of the most exciting areas of probabilistic thinking these days: how causal effects may be defined, observed, and tested in the presence of uncertainty. The chapter summarizes the ongoing scientific debate on this topic and also gives practical illustrations of the most important analyses. Chapter 9, written by Oded Goldreich, presents yet another approach to defining and handling randomness through computational complexity. This approach proves very useful not only in apparently theoretical efforts, such as algorithmic theorem verification, but also in related practical applications, such as cryptography.

The third part considers several applications of probabilistic modeling. Much of the content of the third part describes methods and uses concepts from statistics, but the focus here is not on estimation or testing, although these aspects are also discussed, but rather on model building with the aim of incorporating uncertainty. Chapter 10, written by Michael Lewis, describes the fundamentals of time-series analysis. This approach is used when one has reason to believe that phenomena observed over time are governed not only by the actual status of the population where the observations came from but also by earlier statuses of the same population. Chapter 11, written by Nancy Brandon Tuma, discusses another aspect of the temporal nature of observations, when the information recorded describes the occurrence of certain events of interest. This approach, survival analysis, also referred to as event history analysis, deals with modeling the factors that influence the probability of a certain event occurring within a specific period of time. Chapter 12, written by Jeffrey Wooldridge, deals with sampling and the implications of the sampling procedure for estimation and testing. The discussion goes way beyond elementary simple random sampling and, among other topics, proposes methods for modeling nonresponse. Chapter 13, written by Edward Frees and Jee-Seon Kim, presents another approach to modeling observations over an extended period of time. Particular attention is paid to the advantages and disadvantages of data arising from repeated observations of the same sample (the panel) and to temporal aspects that may be relevant to explain cross-sectional associations. Chapter 14, written by Vasja Vehovar, Metka Zalatel, and Rudi Seljak, deals with probabilistic methods in official statistics. Official statistics has played and continues to play an important role in the development of probabilistic methods for surveys, and the chapter describes the designs of the most frequently carried out surveys by national statistical offices and discusses related issues such as small-area estimation, data fusion, and seam effects. Chapter 15, written by Nick Longford, discusses probabilistic models for measurement error and misclassification. The proposed method of inference considers the true value as a latent variable, and a general solution based on imputation is suggested. Chapter 16, written by Klaas Sijtsma and Wilco Emons, considers a very important case when inference is to be based on imprecise observations: probabilistic developments of tests, in particular for educational purposes, using item response theory. The chapter describes several models and illustrates their applications to real data. Chapter 17, written by Klaus Troitzsch, shows how probabilistic simulation methods may be used to model societal phenomena such as demographic processes or opinion formation. The discussion covers approaches of different complexity, including microsimulation and multi-agent models. Chapter 18, written by Philippa Pattison and Garry Robins, is about the rapidly developing topic of probabilistic network analysis. Probabilistic models are discussed for the evolution of social networks, and several ways for the probabilistic analysis of such networks are described, including simulation methods based on Markov Chain Monte Carlo. Chapter 19, written by Chas Friedman, gives insight into the topic of probabilistic analysis of gambling, a topic that played a very important role in the historic development of probability theory. Several games are investigated, and strategies that are optimal on the average are developed for these. Chapter 20, written by Richard Derrig and Krzyszt of Ostaszewski, describes how probabilistic approaches are applied in insurance. In addition to discussing the most important theoretical aspects of actuarial science, the chapter expands on several theoretical and practical problems of the insurance business. Chapter 21, written by Ad Feelders, discusses probabilistic methods for another financial problem, the scoring of credit applicants. Several models for determining the probability that someone will not pay back a loan are described, and special attention is given to the difficulties arising from the fact that observations are available only for those who were actually given a loan, leading to a special incomplete data problem. Chapter 22, written by Craig Rennie, shows how optimal investment portfolios are designed from risky securities, where risk is measured by the standard deviation of the return of the investment. Among other theories, the famous Black-Sholes option-pricing model is described. Chapter 23, written by George Luger and Chayan Chakrabarti, describes how probabilistic reasoning may be used in achieving automatic decisions. The chapter discusses expert systems and belief networks based on graphical models, showing how the Bayesian approach may lead to simplified and efficient decisions. Chapter 24, written by Julia Mortera and Philip Dawid, discusses how uncertainty related to evidence should be correctly interpreted in criminal investigations. In addition to discussing common mistakes and misinterpretations, they also show how Bayesian networks may be used to interpret complex evidence, including DNA data. Chapter 25, written by Basil C. Bitas, describes practical aspects of the presentation of probabilistic arguments in the courtroom. Science should be interpreted so that it becomes relevant for the law, and in addition to the main aspect of this integration, the prevailing practice in several countries from all over the world is discussed.

An edited volume, like this one, is always the result of the effort of several contributors. First and foremost, I am indebted to all the authors for their contributions and also for their willingness to subject their manuscripts to the several rounds of the review procedure. Perhaps no editor could be equally well qualified in all the fields covered in the Handbook, and I learned a lot while working with the authors. I am also indebted to the members of the Advisory Board, who helped me through several stages of this project. Very special thanks go to Lisa Cuevas Shaw, former Acquisitions Editor at Sage, who first proposed the idea of such a Handbook and applied successful tactics to convince me that I should try to put it together. She also provided me with constant moral support throughout the two years of actual editorial work. I feel fortunate to have been able to work with Sage's production team and, in particular, with Melanie Birdsall and Shankaran Srinivasan, who not only masterly handled the technical aspects of book production but were also very accommodating when it came to consolidating the individual chapters into one volume.

Paul Barrett (Auckland, New Zealand) made a very special contribution to the Handbook by trying to write a chapter on probabilistic profiling in psychology (criminal profiling, executive recruitment, etc). After much effort, he came to the conclusion that very little probability was being actually used in these activities and suggested that we drop the chapter. I thank him for his effort, and perhaps, this could be a new and fruitful field for the application of probabilistic thinking.

My very sad duty is to let the readers of the Handbook know that Professor Chas Friedman (Austin, Texas), author of the chapter on gambling, passed away shortly after completing the manuscript of his contribution, at the age of sixty. Although I have never had a chance to meet Professor Friedman personally, during our collaboration I learned to appreciate his disciplined thinking and wide-ranging scientific interests. This chapter is likely to be his last publication.

The hope, shared, I am sure, by all contributors, that such a Handbook may not only serve as a source of reference but also influence the way scientific research is conducted by some of its readers helped us overcome many difficulties while working on the manuscript. When the work is close to coming to an end, the editor may only wish that many readers will find the effort worthwhile.

Budapest, May 2007

## Acknowledgments

The publisher and the editor wish to express their indebtedness for the unusually helpful, constructive, and encouraging comments from the following reviewers during the planning phase of the book: Michael A. Clump, Marymount University; Robert P. Dobrow, Carleton College; Jeffrey C. Fox, Fort Lewis College; Kosuke Imai, Princeton University; Peter M. Lee, Wentworth College, University of York; Leland G. Neuberg, Boston University; and Timo Seppäläinen, University of Wisconsin-Madison.

Mauro Gasparini Politecnico di Torino, Turin, Italy

Peter Lakner New York University, New York, New York

Nicholas T. Longford SNTL, Leicester, United Kingdom

Paul Shields University of Toledo, Toledo, Ohio

Michael Sobel Columbia University, New York, New York

Rolf Steyer Friedrich-Schiller-Universität, Jena, Germany

Gábor J. Székely Bowling Green Sate University, Bowling Green, Ohio

Graham J. G. Upton University of Essex, Colchester, United Kingdom

Tamás Rudas is Professor of Statistics and Head of the Department of Statistics of the Faculty of Social Sciences, Eötvös Loránd University (ELTE) in Budapest and Director of the Program in Survey Statistics. Currently, he also serves as Dean of the Faculty. He is also Academic Director of the TARKI Social Research Institute. He has held several visiting appointments in the United States, Germany, Austria, Slovenia, and Poland. He is General Secretary of the European Association of Methodology. His main research area is statistics and its applications in the social sciences, especially the analysis of categorical data. Among other topics, he has contributed to the development of methods of measuring model fit and to the theory of marginal models. He has published in many theoretical and methodological journals, including The Annals of Statistics, Journal of the Royal Statistical Society, Sociological Methodology, Communications in Statistics, Journal of Educational and Behavioral Statistics, and Quality and Quantity. He is also the author of Odds Ratios in the Analysis of Contingency Tables (Sage, 1998) and Probability Theory: A Primer (Sage, 2004) and of books in Hungarian, including one (now in its second edition) on opinion polls. Professor Rudas holds a PhD in mathematics (probability theory and mathematical statistics) from the Eötvös Loránd University and a Doctor of Science degree from the Hungarian Academy of Science.

Basil C. Bitas has substantial experience in international legal and business matters, having been both in-house counsel to the Philip Morris Group of Companies in Lausanne, Switzerland, and Managing Partner of the law offices of the U.S. firm Shook, Hardy, & Bacon LLP in Geneva. The nature of his practice has involved intensive interaction with the legal systems, commercial practices, cultures, customs, and citizens of North America, Europe, the Middle East, and Asia. The latter region became a subspecialty of his practice, with particular emphasis on Korea, Japan, and China. His practice background encompasses extensive experience with complex litigation, particularly product liability issues, where he developed a specialty in the use and interpretation of medical and economic statistics in the development and presentation of legal argumentation. More recently, he has been a visiting professor at the Business School of Lausanne and the law faculty of the University of Fribourg in Switzerland as well as a guest speaker at the law faculties of the Catholic University and the Fundaçăo Getulio Vargas in Rio de Janeiro and the Federal University in Porto Alegre, Brazil. He holds bachelor's degrees in history and economics from Brown University in Providence, Rhode Island, having graduated Magna Cum Laude and Phi Beta Kappa in 1981. He also holds a Juris Doctor degree (1987) Cum Laude from Georgetown University Law Center in Washington, D.C., and maintains active bar memberships in the State of New York and Washington, D.C.

Chayan Chakrabarti is at the University of New Mexico. His research interests include artificial intelligence, machine learning, and emergent computing. He was a staff research assistant in the Space Data Systems (ISR-3) group at Los Alamos National Laboratory, where he designed machine-learning algorithms for object recognition in satellite images. He holds a master's degree in computer science from the University of New Mexico and a bachelor's degree in computer engineering from the University of Mumbai (Bombay), India.

Philip Dawid is Professor of Statistics at Cambridge University. From 1989 to 2007, he was Pearson Professor of Statistics at University College London. He is a fellow of the Royal Statistical Society, which has awarded him the Guy Medal in bronze and in silver; elected fellow of the Institute of Mathematical Statistics; elected member of the International Statistical Institute; and member of the Organising Committee for the Valencia International Meetings on Bayesian Statistics. He has served as editor of Journal of the Royal Statistical Society Series B, Biometrika, and Bayesian Analysis and as president of the International Society for Bayesian Analysis. His research focuses on the foundations of statistics, with emphasis on the Bayesian approach. His coauthored book Probabilistic Networks and Expert Systems (1999) won the 2002 DeGroot Prize. He is interested in the logical problems of structuring legal evidence and led an international research project applying Bayesian networks to complex cases of forensic identification from DNA profiles. He recently directed a multidisciplinary research program, Evidence, Inference and Enquiry, at University College London.

Richard A. Derrig, PhD, is President of OPAL Consulting LLC of Providence, Rhode Island, providing research and regulatory support to the property/casualty insurance industry. Prior to forming OPAL in 2004, he held various positions with the Automobile Insurers Bureau (AIB) and the Insurance Fraud Bureau (IFB) of Massachusetts for over 27 years, retiring as senior Vice President of AIB and Vice President, Research of IFB. He was a visiting scholar during 2004–2007 in the Department of Insurance and Risk Management at the Wharton School, University of Pennsylvania and was an adjunct professor for spring 2006. He has had a career-long affinity with probability theory, beginning with his doctoral thesis in mathematics at Brown University, on ergodic theory and operator algebras, and continuing with papers on insurance finance and economics, applications of fuzzy set theory, and, currently, predictive modeling or data mining, published in The Journal of Risk and Insurance, North American Actuarial Journal, Proceedings of the Casualty Actuarial Society, Risk Management and Insurance Review, and others.

Wilco H. M. Emons is an assistant professor at the Department of Methodology and Statistics, Faculty of Social Sciences, Tilburg University, the Netherlands. His main scientific interests cover psychometric and measurement issues in psychological assessment, including test development, (non) parametric item response theory models, person-fit analysis, detection and diagnosis of aberrant response behavior, and measurement in medical and health psychology. His work has appeared in Applied Psychological Measurement, Journal of Psychosomatic Research, Multivariate Behavioral Research, and Psychological Methods. He holds a PhD from the University of Tilburg, The Netherlands.

Ad Feelders is an assistant professor at the Department of Information and Computing Sciences of Utrecht University in The Netherlands. He has worked as a consultant for a data-mining company, where he was in charge of projects for banks and insurance companies. Before coming to Utrecht, he was an assistant professor at the Department of Economics of Tilburg University. He has published several articles on data mining and credit scoring in international conference proceedings and journals. He is a member of the editorial board of the International Journal of Intelligent Systems in Accounting, Finance and Management.

Edward W. Frees is a professor of business and statistics at the University of Wisconsin-Madison and is holder of the Assurant Health Insurance Professorship of Actuarial Science. He is a fellow of both the Society of Actuaries and the American Statistical Association. He has published two books, Data Analysis Using Regression Models (1996) and Longitudinal and Panel Data: Analysis and Applications for the Social Sciences (2004). He has served as editor of the North American Actuarial Journal and is currently an associate editor for Insurance: Mathematics and Economics. His research interests include actuarial science, regression, and modeling of complex data sets.

Herwig Friedl is a professor of statistics at the Graz University of Technology, Austria. Since 2004 he has been the editor of Austrian Journal of Statistics, and since 2006 he additionally serves as coeditor of Statistical Modelling: An International Journal. Currently, he is also the secretary of the Statistical Modelling Society. His recent research interest is in generalized linear models with random effects, and he has published his work in Biometrics, Computational Statistics, Applied Statistics, and Environmetrics, among others.

Chas Friedman was a professor of mathematics at the University of Texas-Austin. His early interests included mandolin building, tuba playing, and mathematics. He decided on the latter, attending the Graduate School at Princeton, which resulted in a PhD in 1971. He spent two years as an instructor at the Massachusetts Institute of Technology, and then went to the University of Texas-Austin in 1973. His professional interests included mathematical physics, differential equations, and probability, and he published articles on these subjects and others (e.g., number theory). He resided in the Texas Hill Country near San Marcos and Wimberley with his wife, five dogs, six cats, two miniature goats, and a pot-bellied pig. In his spare time, he played various instruments, did woodworking and made jewelry, played poker with the local gamblers, and thought about mathematics and its applications. Professor Friedman passed away before this book went to press.

Mauro Gasparini is a professor of statistics at Politecnico di Torino, and he has been teaching engineers since 1999. From 1996 to 1999, he was a senior statistician at Novartis Pharma, Basel, working in PK/PD modeling, Phase I and Phase II trials, and pharmacoepidemiology and offering statistical consulting to production. From 1992 to 1996, he taught statistics at Purdue University as a visiting assistant professor. He has been consulting with Novartis Pharma in Basel and in Milan, Schering Berlin, RAI (the Italian public television), San Raffaele in Milan, and the Istituto Tumori Toscano in Florence. He has received grants from the Italian Ministry of Research and the European Commission. His main publications include papers in The Annals of Statistics, Biometrics, and Journal of Statistical Planning and Inference, among others. He received his PhD in statistics in 1992 at The University of Michigan, where his advisor was Michael Woodroofe.

Oded Goldreich is a professor of mathematics and computer science at the Weizmann Institute of Science (Israel), where he is the incumbent of the Meyer W. Weisgal Professorial Chair. He is a corresponding fellow of the Bavarian Academy of Sciences and Humanities. He was a postdoctoral fellow at the Massachusetts Institute of Techonology's Laboratory for Computer Science from 1983 to 1986. He is the author of the book Modern Cryptography, Probabilistic Proofs and Pseudorandomness (1999) and the two-volume work Foundations of Cryptography (2001 and 2004). He is the editor of Journal of Cryptology, Computational Complexity, and SIAM Journal on Computing and was an invited speaker at various conferences, including the International Congress of Mathematicians (ICM), 1994, and the Crypto97 conference. He received BA, MSc, and DSc degrees in computer science at the Technion-Israel Institute of Technology in 1980, 1982, and 1983, respectively.

Siegfried Hörmann is a scientific assistant at the Institute of Statistics, Graz University of Technology. In the near future, he will hold an appointment as an assistant professor at the University of Utah. His main research interests are probability theory, time-series analysis, and applied statistics. He is especially interested in the asymptotic theory of dependent random processes. He has published in Journal of Theoretical Probability, Probability and Mathematical Statistics, Statistics and Probability Letters, among others. He finished his PhD under the supervision of Prof. István Berkes in November 2006.

Jee-Seon Kim is Associate Professor of Quantitative Methods in the Department of Educational Psychology at the University of Wisconsin-Madison. Her research interests concern the development and application of quantitative methods in education and the social sciences, especially focusing on multilevel models and other latent variable models; methods for modeling change, learning, and human development using longitudinal data; categorical data analysis; and issues related to omitted variables, test equating, and school effectiveness. Her scholarly work has been published in Psychometrika, Multivariate Behavioral Research, Journal of Educational Measurement, British Journal of Mathematical and Statistical Psychology, Educational Measurement: Issues and Practice, Applied Psychological Measurement, and Psychological Methods. She received the Outstanding Dissertation Award for Quantitative Methods from the American Education Research Association in 2002 and was selected as a fellow by the National Academy of Education and Spencer Foundation in 2004.

Igor Kopylov is an assistant professor at the Department of Economics, University of California, Irvine. He is also affiliated with the Institute of Mathematical Behavioral Sciences. He has done research mainly in decision theory. In his doctoral thesis, he studied the extent to which subjective probabilities are used under Knightian ambiguity. More recently, he has focused on modeling choice in the presence of costly emotions, such as temptation and guilt. He has published in Journal of Economic Theory. He received his PhD in Economics at the University of Rochester in 2003 under the supervision of Larry Epstein.

Peter M. Lee has recently retired from the Department of Mathematics in the University of York, United Kingdom, after 33 years (but is still there from time to time). Before that, he was a fellow of Peterhouse, Cambridge. His main interests are in Bayesian statistics and the history of statistics. He is the author of Bayesian Statistics: An Introduction (now in its third edition).

Michael Anthony Lewis is an associate professor at the Stony Brook University School of Social Welfare and visiting professor at the Hunter College School of Social Work. His main areas of interest are poverty/inequality, civic participation, and (recently) the environment. He is the coauthor of Economics for Social Workers and the coeditor of The Ethics and Economics of the Basic Income Guarantee. His work has also appeared in The Journal of Sociology and Social Welfare, The Journal of Socio-Economics, Review of Social Economy, The Journal of Poverty, Social Work in Health Care, Rutgers School of Law Journal of Law and Urban Policy, and International Journal of Environment, Workplace, and Employment.

Nicholas T. Longford is the Director of SNTL, a statistical research and consulting company in Reading, England. Previously, until 2004, he was a senior research fellow in statistics at De Montfort University, Leicester, England. His areas of specialization are multilevel analysis, missing data, small-area estimation, and model uncertainty. He has several publications in Journal of the Royal Statistical Society, Survey Methodology, Statistics in Medicine, Computational Statistics and Data Analysis, and Psychometrika. He is the author of three monographs, Random Coefficient Models (1993), Models for Uncertainty in Educational Testing (1995), and Missing Data and Small-Area Estimation (2005). He was the first Campion Fellow, an award received for collaboration between academic and official statistics (2000–2002). He is a former president of the Princeton-Trenton Chapter of the American Statistical Association.

George Luger has been a professor in the University of New Mexico Computer Science Department since 1979. George Luger had a five-year postdoctoral research appointment at the Department of Artificial Intelligence of the University of Edinburgh in Scotland, where he worked on several early expert systems, participated in development and testing of the Prolog computer language, and carried out research on the computational modeling of human problem-solving performance. At the University of New Mexico, George Luger has also been made a professor in the Psychology and Linguistics Departments, reflecting his interdisciplinary research and teaching in these areas. His most recent research, supported by the National Science Foundation, is in diagnostic reasoning, where he has developed stochastic models, mostly in an extended form of Bayesian belief networks. His book Cognitive Science was published in 1994. His other book, Artificial Intelligence: Structures and Strategies for Complex Problem Solving (2005), is now in its fifth edition. His two master's degrees are in pure and applied mathematics. He received his PhD from the University of Pennsylvania in 1973, with a dissertation focusing on the computational modeling of human problem-solving performance in the tradition of Allen Newell and Herbert Simon.

Julia Mortera is a professor of statistics at Università Roma Tre and director of the PhD program in “Statistical Methodology for Economics and Business.” Her current research interests are in probabilistic expert systems for analyzing complex forensic DNA identification cases, including paternity testing and DNA mixtures, and in object-oriented Bayesian networks and their applications. Her publications have appeared in Biometrika, Forensic Science International, Theoretical Population Biology, Journal of the Royal Statistical Society Series B, Journal of the American Statistical Association, Scandinavian Journal of Statistics, Journal of Statistical Planning and Inference, Management Science, Bayesian Analysis, International Statistical Review, TEST, and Uncertainty in Artificial Intelligence. She is an associate editor of Bayesian Analysis. She was the principal scientific organizer of the 5th International Conference on Forensic Statistics and is a member of the Organising Committee for the International Conference on Forensic Inference and Statistics. She has coordinated research grants from EU, MIUR, and CNR and was local coordinator for the DNA Forensic Research Interchange Grant of the Leverhume Trust.

Anthony O'Hagan is a professor of statistics at the University of Sheffield, United Kingdom. He is a fellow of the Royal Statistical Society and has served on the Society's Council and Research Section. His research is on the methodology and applications of Bayesian statistics. On the methodological side, his principal areas of active research are in the elicitation of expert judgments and in characterizing the uncertainty in mechanistic process models (such as models of climate, aero-engines, proteins, or hydrology). His applied work is wide-ranging, including water supply systems, auditing, and archaeology, but most recently, it has focused on health economics. Tony has published in most of the leading statistics journals, as well as journals in other fields. He has also written or cowritten six books. Bayesian Inference (Volume 2b in Kendall's Advanced Theory of Statistics, 2006; coauthor Jonathan Forster) is one of the leading graduate texts in the field. His latest book, Uncertain Judgements (2007; seven coauthors), is the most systematic and comprehensive text on elicitation of expert probability judgments to date.

Krzysztof Ostaszewski is Actuarial Program Director and a professor of mathematics at Illinois State University in Normal, Illinois. His main areas of research are asset-liability management for insurance enterprises and other financial intermediaries, and connections between microeconomics, especially price theory, and actuarial science, insurance, and investments. He is a chartered financial analyst, a member of the American Academy of Actuaries, and a fellow of the Society of Actuaries. He was a Fulbright Research Fellow in 1995 and a Fulbright Senior Specialist in 2003–2004. He received, jointly with Richard Derrig, the 2005 Mehr Award of the American Risk and Insurance Association. He also won the Hardigree Award of the Western Risk and Insurance Association for the best research paper published in 2003 in Journal of Insurance Issues. He has authored six research monographs published by the American Mathematical Society, Society of Actuaries, Elsevier, and Wydawnictwa Naukowo-Techniczne in Poland; as well as several other books, including five volumes of poetry. His research works in mathematics have appeared in journals such as the Proceedings of the American Mathematical Society, Forum Mathematicum, and Journal of Mathematical Analysis and Applications. His works in economics appeared in American Economic Review and Journal of Business. His research in actuarial science has been published in The Journal of Risk and Insurance, North American Actuarial Journal, Proceedings of the Casualty Actuarial Society, Journal of Insurance Issues, and other journals. He has worked in asset-liability management and modeling, as well as investment management, at Hartford Life, Providian Capital Management, and his private consulting practice. He holds a PhD in mathematics from the University of Washington in Seattle.

Philippa Pattison is a professor in the Department of Psychology and President of the Academic Board at the University of Melbourne. Her research is focused on the development of statistical models for networks and on network-based social processes and on applications of these models to a diverse range of phenomena. Recent publications have appeared in journals such as Sociological Methodology, American Journal of Sociology, Social Networks, and Organization Science. She is also a contributor to Models and Methods in Social Network Analysis and to Dictionary of Economics. Philippa was elected a fellow of the Academy of Social Sciences in Australia in 1994.

Craig G. Rennie is an associate professor of finance in the Sam M. Walton College of Business, University of Arkansas, where he holds the appointment of Brewer Professor of Business/Financial Markets. He has authored numerous scholarly articles in finance and has published or has forthcoming papers in The Journal of Business, Journal of Financial Research, The Financial Review, European Financial Management, and Southern Business and Economic Journal. He has served as reviewer for three peer-reviewed journals and presented cutting-edge finance research at international, national, and regional conferences. He currently teaches applied portfolio management at the graduate and undergraduate levels, consults in the investments industry, and is faculty advisor for the third oldest and one of the largest student-managed investment funds in the world. His students regularly outperform the S&P 500 while managing a large portfolio of stocks, bonds, funds, and derivatives. He holds a PhD in finance from the University of Oregon.

Garry Robins is an associate professor in the Department of Psychology, School of Behavioural Science at the University of Melbourne, Australia. His research concentrates on the development of social network methodologies and their application in a wide number of empirical projects. His research has won awards from the Psychometric Association and the American Psychological Association. He is a Linton Freeman Award winner for significant contributions to the scientific study of social structure. He is the editor of Journal of Social Structure and a member of the Board of the International Network for Social Network Analysis. Recent publications have appeared in journals such as Sociological Methodology, American Journal of Sociology, and Social Networks.

Maria Piera Rogantin is currently Associate Professor of Statistics in the Department of Mathematics at the University of Genoa, where she has major responsibilities for the Mathematical Statistics and Information Processing program. She has taught a vast range of statistics and probability courses for undergraduate degrees, master's degrees, and training courses. Her research interest concerns the investigation of theoretical problems and the construction of statistical and probabilistic models. She has worked in design of experiments, survival analysis, time series, multivariate analysis, and survey analysis. Various consulting projects allowed the applications of her results in industry, psychometrics, medicine, meteorology, and e-consulting. Her methodological research uses mathematical theory developed in nonstatistical research framework for statistical modeling, in particular differential geometry for information geometry and commutative algebra for algebraic statistics. She has a degree in mathematics, summa cum laude, from the University of Genoa.

Rudi Seljak works as Head of the Department for Sampling and Survey Methodology at the Statistical Office of the Republic of Slovenia. His background is mathematics, and he has theoretical and practical experience in the field of survey sampling. He has actively taken part in many international conferences and published in this area. He was also a member of the program committee of the European Conference on Quality in Survey Statistics, Cardiff, 2006. He has a BSc in mathematics from the Faculty of Mathematics, University Ljubljana.

Nicholas Shackel is James Martin Research Fellow in Theoretical Ethics at the Future of Humanity Institute, Faculty of Philosophy and James Martin 21st Century School, University of Oxford. Dr. Shackel is a philosopher. His interests include ethics, epistemology, philosophy of mind, philosophy of mathematics, and logic. He has conducted research on the relations between practical and theoretical reason, and paradoxes, including paradoxes of rational decision, philosophy of probability, intentionality, and deontic logic. His publications include papers in Analysis, British Journal for the Philosophy of Science, Erkenntnis, Metaphilosophy, and Philosophy of Science and Mind.

Klaas Sijtsma is Professor of Methodology of Psychological Research at Tilburg University, Tilburg, The Netherlands. He is Head of the Department of Methodology and Statistics, Faculty of Social Sciences, Tilburg University, and also Chair of the Committee on Psychological Testing in The Netherlands (COTAN) of the NIP, the Dutch professional association of psychologists. Dr. Sijtsma's scientific interest concentrates on the measurement of individual differences with respect to psychological constructs. His research covers topics such as reliability of measurement and scalability of items, theoretical properties and goodness-of-fit investigation of item response models, person-fit analysis, item selection, models for cognitive processes underlying item responses, analysis of missing item scores, and detection of outliers. Dr. Sijtsma is a member of the editorial boards of Applied Psychological Measurement and Psychometrika. He has published in Applied Psychological Measurement, British Journal of Mathematical and Statistical Psychology, Multivariate Behavioral Research, Psychological Methods, and Psychometrika. He is the coauthor of two textbooks, one on psychological test theory and the other on nonparametric item response theory. He has a PhD from the University of Groningen, The Netherlands.

Michael Sobel is a professor at Columbia University. He has published extensively in the social sciences and statistics and is a past editor of Sociological Methodology. His current interests include causal inference, especially when interference is present, as in neighborhood effects, and methods of election forecasting.

Klaus G. Troitzsch has been a professor of computer applications in the social sciences at the University of Koblenz-Landau since 1986. His main interests in teaching and research are social science methodology and, especially, modeling and simulation in the social sciences. He was among the signatories of the European Social Simulation Association (ESSA) and acts as its treasurer and webmaster. He has been involved in several international projects, for example, those devoted to curriculum development in social science methodology, during which he organized summer schools, particularly in social simulation, which continue to be offered in close cooperation with Nigel Gilbert, University of Surrey, United Kingdom. Current projects are devoted to analyzing traffic route decisions, to microsimulation analysis of the marriage between different ethnic groups in New Zealand, and to the simulation of emerging norms in social systems. He is author, coauthor, and coeditor of a number of books on simulation, has authored several articles on social simulation, and organized or co-organized many national and international conferences on social simulation.

Nancy Brandon Tuma is a professor of sociology at Stanford University and was the 2003–2005 Director of Stanford's Program on Urban Studies. She is a leading sociological methodologist who has focused primarily on models and methods for studying change. In 1994, she was awarded the Lazarsfeld award for her contributions to sociological methodology. She has served as editor of Sociological Methodology and also as associate editor of Journal of the American Statistical Association. Best known as the coauthor of Social Dynamics: Models and Methods (1984), a pioneering book on event history analysis, she has also developed models for diffusion processes that are extensions of event history models. In addition, she has published studies of life careers and social inequalities in the United States, Germany, China, Poland, the Soviet Union, and various countries formerly part of the Soviet Union. Her primary research interest currently is the impact of the transition from socialism on people's life careers. She recently coauthored an article on household power and decision making of married women in Tajikistan. She has a BA with distinction in mathematics and chemistry from Cornell University, an MA in biochemistry from the University of California at Berkeley, and a PhD in sociology from Michigan State University.

Vasja Vehovar is a professor of statistics at the Faculty of Social Sciences, University of Ljubljana, Slovenia. He teaches courses on Sampling, Survey Methodology, and Information Society. He has been a survey sampling consultant for various academic, commercial, and official surveys and also serves as a member of the Methods Group of the European Social Survey (ESS). He has published chapters in monographs of leading publishers and also published scholarly articles in leading journals such as Journal of Official Statistics and Journal of the American Statistical Association. In addition, he is developing the WebSM portal (http://www.websm.org) that is devoted to Web survey methodology and was the coordinator of the corresponding EU framework project. Since 1996, he has been the principal investigator of the Research on the Internet in Slovenia project (http://www.ris.org), which is today the leading source for information society research in Slovenia.

Jeffrey M. Wooldridge is University Distinguished Professor of Economics at Michigan State University, where he has taught since 1991. He previously taught at the Massachusetts Institute of Technology. He is a fellow of the Econometric Society and of Journal of Econometrics. His other awards include the Plura Scripset award from Econometric Theory and the Sir Richard Stone prize from Journal of Applied Econometrics. He has also served on several editorial boards, including as editor of Journal of Business and Economic Statistics. He has written chapters for the Handbook of Econometrics and the Handbook of Applied Econometrics. He is the author of Introductory Econometrics: A Modern Approach (third edition, 2006) and Econometric Analysis of Cross Section and Panel Data (2002). He received his bachelor of arts, with majors in computer science and economics, from the University of California, Berkeley, and his doctorate in economics from the University of California, San Diego.

Matka Zaletel works as Director of the Section for General Methodology and Standards at the Statistical Office of the Republic of Slovenia. She has a long theoretical and practical experience in sampling surveys and in the field of quality of statistical data. She has also been involved in many infrastructural projects at the Statistical Office of the Republic of Slovenia. She has actively participated in many international conferences related to official statistics and published in these areas. Her background is mathematics (she has a BSc from the Faculty of Mathematics, University of Ljubljana), and she received a postgraduate diploma in Social Science Data Analysis at the University of Essex, United Kingdom.