Probability and Conditional Expectation

Wiley Series in Probability and Statistics

Book 5
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Probability and Conditional Expectations bridges the gap between books on probability theory and statistics by providing the probabilistic concepts estimated and tested in analysis of variance, regression analysis, factor analysis, structural equation modeling, hierarchical linear models and analysis of qualitative data. The authors emphasize the theory of conditional expectations that is also fundamental to conditional independence and conditional distributions.

Probability and Conditional Expectations

  • Presents a rigorous and detailed mathematical treatment of probability theory focusing on concepts that are fundamental to understand what we are estimating in applied statistics.
  • Explores the basics of random variables along with extensive coverage of measurable functions and integration.
  • Extensively treats conditional expectations also with respect to a conditional probability measure and the concept of conditional effect functions, which are crucial in the analysis of causal effects.
  • Is illustrated throughout with simple examples, numerous exercises and detailed solutions.
  • Provides website links to further resources including videos of courses delivered by the authors as well as R code exercises to help illustrate the theory presented throughout the book.
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About the author

Rolf Steyer,
Institute of Psychology, University of Jena, Germany

Werner Nagel,
Institute of Mathematics, University of Jena, Germany

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Additional Information

Publisher
John Wiley & Sons
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Published on
Mar 10, 2017
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Pages
600
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ISBN
9781119243489
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Language
English
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Genres
Mathematics / Probability & Statistics / General
Mathematics / Probability & Statistics / Stochastic Processes
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Content Protection
This content is DRM protected.
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Available on Android devices
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Presents elements of clinical trial methods that are essential in planning, designing, conducting, analyzing, and interpreting clinical trials with the goal of improving the evidence derived from these important studies

This Third Edition builds on the text’s reputation as a straightforward, detailed, and authoritative presentation of quantitative methods for clinical trials. Readers will encounter the principles of design for various types of clinical trials, and are then skillfully guided through the complete process of planning the experiment, assembling a study cohort, assessing data, and reporting results. Throughout the process, the author alerts readers to problems that may arise during the course of the trial and provides common sense solutions. All stages of therapeutic development are discussed in detail, and the methods are not restricted to a single clinical application area.

The authors bases current revisions and updates on his own experience, classroom instruction, and feedback from teachers and medical and statistical professionals involved in clinical trials. The Third Edition greatly expands its coverage, ranging from statistical principles to new and provocative topics, including alternative medicine and ethics, middle development, comparative studies, and adaptive designs. At the same time, it offers more pragmatic advice for issues such as selecting outcomes, sample size, analysis, reporting, and handling allegations of misconduct. Readers familiar with the First and Second Editions will discover revamped exercise sets; an updated and extensive reference section; new material on endpoints and the developmental pipeline, among others; and revisions of numerous sections.

In addition, this book:

• Features accessible and broad coverage of statistical design methods—the crucial building blocks of clinical trials and medical research -- now complete with new chapters on overall development, middle development, comparative studies, and adaptive designs

• Teaches readers to design clinical trials that produce valid qualitative results backed by rigorous statistical methods

• Contains an introduction and summary in each chapter to reinforce key points

• Includes discussion questions to stimulate critical thinking and help readers understand how they can apply their newfound knowledge

• Provides extensive references to direct readers to the most recent literature, and there are numerous new or revised exercises throughout the book

Clinical Trials: A Methodologic Perspective, Third Edition is a textbook accessible to advanced undergraduate students in the quantitative sciences, graduate students in public health and the life sciences, physicians training in clinical research methods, and biostatisticians and epidemiologists.

This book is accompanied by downloadable files available below under the DOWNLOADS tab.

These files include:

MATHEMATICA program – A set of downloadable files that tracks the chapters, containing code pertaining to each. SAS PROGRAMS and DATA FILES used in the book.

The following software programs, included in the downloadables, were developed by the author, Steven Piantadosi, M.D., Ph.D:

RANDOMIZATION – This program generates treatment assignments for a clinical trial using blocked stratified randomization. CRM – Implements the continual reassessment methods for dose finding clinical trials. OPTIMAL – Calculates two-stage optimal phase II designs using the Simon method. POWER – This is a power and sample size program for clinical trials.

Executables for installing these programs can also be found at https://risccweb.csmc.edu/biostats/.

Steven Piantadosi, MD, PhD, is the Phase One Foundation Distinguished Chair and Director of the Samuel Oschin Cancer Institute, and Professor of Medicine at Cedars-Sinai Medical Center in Los Angeles, California. Dr. Piantadosi is one of the world’s leading experts in the design and analysis of clinical trials for cancer research. He has taught clinical trials methods extensively in formal courses and short venues. He has advised numerous academic programs and collaborations nationally regarding clinical trial design and conduct, and has served on external advisory boards for the National Institutes of Health and other prominent cancer programs and centers. The author of more than 260 peer-reviewed scientific articles, Dr. Piantadosi has published extensively on research results, clinical applications, and trial methodology. While his papers have contributed to many areas of oncology, he has also collaborated on diverse studies outside oncology including lung disease and degenerative neurological disease.

This accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving

Simulation and the Monte Carlo Method, Third Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples.

The Third Edition features a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. A second new chapter introduces the stochastic enumeration method, which is a new fast sequential Monte Carlo method for tree search. In addition, the Third Edition features new material on:

• Random number generation, including multiple-recursive generators and the Mersenne Twister

• Simulation of Gaussian processes, Brownian motion, and diffusion processes

• Multilevel Monte Carlo method

• New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters

• Over 100 algorithms in modern pseudo code with flow control

• Over 25 new exercises

Simulation and the Monte Carlo Method, Third Edition is an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

Reuven Y. Rubinstein, DSc, was Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein was also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting.

Dirk P. Kroese, PhD, is a Professor of Mathematics and Statistics in the School of Mathematics and Physics of The University of Queensland, Australia. He has published over 100 articles and four books in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic c theory, reliability, computational statistics, applied probability, and stochastic modeling.

Provides a one-stop resource for engineers learning biostatistics using MATLAB® and WinBUGS

Through its scope and depth of coverage, this book addresses the needs of the vibrant and rapidly growing bio-oriented engineering fields while implementing software packages that are familiar to engineers. The book is heavily oriented to computation and hands-on approaches so readers understand each step of the programming. Another dimension of this book is in parallel coverage of both Bayesian and frequentist approaches to statistical inference. It avoids taking sides on the classical vs. Bayesian paradigms, and many examples in this book are solved using both methods. The results are then compared and commented upon. Readers have the choice of MATLAB® for classical data analysis and WinBUGS/OpenBUGS for Bayesian data analysis. Every chapter starts with a box highlighting what is covered in that chapter and ends with exercises, a list of software scripts, datasets, and references.

Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS also includes:

parallel coverage of classical and Bayesian approaches, where appropriate substantial coverage of Bayesian approaches to statistical inference material that has been classroom-tested in an introductory statistics course in bioengineering over several years exercises at the end of each chapter and an accompanying website with full solutions and hints to some exercises, as well as additional materials and examples

Engineering Biostatistics: An Introduction using MATLAB® and WinBUGS can serve as a textbook for introductory-to-intermediate applied statistics courses, as well as a useful reference for engineers interested in biostatistical approaches.

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 --Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory--Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Fsehbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Gerald d. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I--Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II--Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1--Power Series--lntegration--Conformal Mapping--Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2--Special Functions--Integral Transforms--Asymptotics--Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3--Discrete Fourier Analysis--Cauchy Integrals--Construction of Conformal Maps--Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochetadt Integral Equations Erwin O. Kreyezig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation All Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P.M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I--Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II--Automorphic and Abelian integrals C. L Siegel Topics in Complex Function Theory, Volume III--Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems
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