free statistical eBook

" Monte Carlo Methods"
Wiley-Interscience (October 15, 1986) | ISBN: 0471898392 | 208 pages | PDF | 6,2 Mb

This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks.
The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the ¿Metropolis algorithm¿ in the context of sampling methods, clearly distinguishing it from importance sampling.

Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.

Gary L. Wise, Eric B. Hall "Counterexamples in Probability and Real Analysis"
Oxford University Press, USA | 1993-09-11 | ISBN:0195070682 | 224 pages | Djvu | 4,2 Mb

A counterexample is any example or result that is the opposite of one's intuition or to commonly held beliefs. Counterexamples can have great educational value in illuminating complex topics that are difficult to explain in a rigidly logical, written presentation. For example, ideas in mathematical sciences that might seem intuitively obvious may be proved incorrect with the use of a counterexample. This monograph concentrates on counterexamples for use at the intersection of probability and real analysis, which makes it unique among such treatments. The authors argue convincingly that probability theory cannot be separated from real analysis, and this book contains over 300 examples related to both the theory and application of mathematics. Many of the examples in this collection are new, and many old ones, previously buried in the literature, are now accessible for the first time. In contrast to several other collections, all of the examples in this book are completely self-contained--no details are passed off to obscure outside references. Students and theorists across fields as diverse as real analysis, probability, statistics, and engineering will want a copy of this book.

Ken Binmore"Playing for Real: A Text on Game Theory"
Oxford University Press, USA | 2007-03-02 | ISBN: 0195300572 | 656 pages | PDF | 5,5 Mb

Ken Binmore's previous game theory textbook, Fun and Games (D.C. Heath, 1991), carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that game theory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but changes the organization to match how game theory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in game theory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists.

Dirk Aeyels, F. Lamnabhi Lagarrigue, Arjan Van Der Schaft "Stability and Stabilization of Nonlinear Systems "
Springer | 1999-09 | ISBN:1852336382 | 387 pages | PDF | 2,6 Mb


These papers were presented at the first EC-TMR Nonlinear Control Network Workshop, on Stability and Stabilization of Nonlinear Systems, that took place in March 1999, Ghent, Belgium. The TMR programme offers a unique opporuntity for the academic community to expand their knowledge, share their experience and identify and discuss strategic issues in aspects of nonlinear control engineering. The aim is to create a resource centre of available expertise and research interests. This outstanding reference volume presents current and emerging research directions, including: Stability analysis of nonlinear dynamical systems and converse Lyapunov theorems; Stabilization and regulation of nonlinear dynammical control systems; Control of physical systems using physics-based Lyapunov functions and passivity, as well as birfucation analysis and optimal control. This collection of peer-reviewed papers provides a comprehensive overview of this field of research for graduate students and researchers in engineering and applied mathematics.

Introduction to Random Processes
by William A. Gardner
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Data Manipulation with R (Use R)
by Phil Spector

Publisher: Springer
Number Of Pages: 154
Publication Date: 2008-03-19
ISBN-10 / ASIN: 0387747303
ISBN-13 / EAN: 9780387747309
Binding: Paperback


Product Description:



Since its inception, R has become one of the preeminent programs for statistical computing and data analysis. The ready availability of the program, along with a wide variety of packages and the supportive R community make R an excellent choice for almost any kind of computing task related to statistics. However, many users, especially those with experience in other languages, do not take advantage of the full power of R. Because of the nature of R, solutions that make sense in other languages may not be very efficient in R. This book presents a wide array of methods applicable for reading data into R, and efficiently manipulating that data.

In addition to the built-in functions, a number of readily available packages from CRAN (the Comprehensive R Archive Networkdata management tasks. ) are also covered. All of the methods presented take advantage of the core features of R: vectorization, efficient use of subscripting, and the proper use of the varied functions in R that are provided for common

Most experienced R users discover that, especially when working with large data sets, it may be helpful to use other programs, notably databases, in conjunction with R. Accordingly, the use of databases in R is covered in detail, along with methods for extracting data from spreadsheets and datasets created by other programs. Character manipulation, while sometimes overlooked within R, is also covered in detail, allowing problems that are traditionally solved by scripting languagesmodeling and graphics functions need their data presented in a data frame, techniques for converting the output of commonly used functions to data frames are provided throughout the book. to be carried out entirely within R. For users with experience in other languages, guidelines for the effective use of programming constructs like loops are provided. Since many statistical

Using a variety of examples based on data sets included with R, along with easily simulated data sets, the book is recommended to anyone using R who wishes to advance from simple examples to practical real-life data manipulation solutions.

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Statistical Mathematics
by A. C. Aitken
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James B. Anderson "Quantum Monte Carlo: Origins, Development, Applications"
Oxford University Press, USA | 2007-02-26 | ISBN:0195310101 | 198 pages | PDF | 7 Mb


Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and straightforward and rooted in statistics and probability theory, their defining characteristic being that the methodology relies on random or pseudo-random sequences of numbers. It is a technique of numerical analysis based on the approximate solution of a problem using repeated sampling experiments and observing the proportion of times a given property is satisfied. The term Monte Carlo was first used to describe calculational methods based on chance in the 1940s, but the methods themselves preceded the term by as much as a century. Quantum Monte Carlo (QMC) first appeared in 1982 and similarly was preceded by development of the related calculational methodology. The success of QMC methods over the past few decades has been remarkable, and this book will clearly demonstrate that success in its discussion of applications. For isolated molecules, the basic material of chemistry, QMC methods have produced exact solutions of the Schroedinger equation for very small systems and the most accurate solutions available for very large systems. The range of applications is impressive: folding of protein molecules, interactions in liquids, structure modeling in crystals and enzymes, quantum dots, designing heat shields and aerodynamic forms, architecture, design, business and economics, and even cinema and video games (3D modeling). This book takes a similar approach to Henry Schaefers classic book Quantum Chemistry (OUP, 1984 now a Dover edition), collecting summaries of some of the most important papers in the quantum Monte Carlo literature, tying everything together with analysis and discussion of applications. Quantum Monte Carlo is a reference book for quantum Monte Carlo applications, belonging near the desk of every quantum chemist, physicist, and a wide range of scientists and engineers across many disciplines, destined to become a classic

Limit Distributions for Sums of Independent Random Variables. Revised Edition
By B. V. Gnedenko, A. N. Kolmogorov


Publisher: Addison-Wesley
Number Of Pages:
Publication Date: 1968
ISBN-10 / ASIN: B000WSX412
ISBN-13 / EAN:
Binding: Hardcover
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Geoffrey R. Grimmett, David R. Stirzaker "One Thousand Exercises in Probability "
Oxford University Press, USA | 2001-07-10 | ISBN:0198572212 | 448 pages | Djvu | 7,1 Mb


This book is a revised, updated and greatly expanded version of the authors' "Probability and Random Processes: Problems and Solutions", first published in 1992. The 1000+ exercises contained within are not merely drill problems but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the student. Topics cover a broad range of subjects, including: elementary aspects of probability and random variables; sampling; Markov chains; convergence; stationary processes; renewals; queues; Martingales; diffusion; mathematical finance and the Black-Scholes model. This text is intended for general use, and to serve students as a companion text for elementary, intermediate and advanced courses in probability and random processes. Useful for anyone needing a large source of problems in these areas and at all levels. This book also acts as a companion volume to the new edition of Probability and Random Processes 3/e, (OUP - 2001), providing the solutions for the problems and exercises

Kerson Huang "Introduction to Statistical Physics"
CRC | 2001-11-15 | ISBN:0748409424 | 400 pages | Djvu | 1,7 Mb

Statistical physics is a core component of most undergraduate (and some post-graduate) physics degree courses. It is primarily concerned with the behavior of matter in bulk-c. Ultimately, it seeks to uncover the laws governing random processes, such as the snow on your TV screen. This essential new textbook guides the reader quickly and critically through a statistical view of the physical world, including a wide range of physical applications to illustrate the methodology. It moves from basic examples to more advanced topics, such as broken symmetry and the Bose-Einstein equation. To accompany the text, the author, a renowned expert in the field, has written a Solutions Manual/Instructor's Guide, available free of charge to lecturers who adopt this book for their courses. Introduction to Statistical Physics will appeal to students and researchers in physics, applied mathematics and statistics.

Michael B. Marcus, Jay Rosen "Markov Processes, Gaussian Processes, and Local Times"
Cambridge University Press | 2006-07-24 | ISBN:0521863007 | 630 pages | PDF | 3,2 Mb


Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including sample path properties. It then proceeds to more advanced results, bringing the reader to the heart of contemporary research. It presents the remarkable isomorphism theorems of Dynkin and Eisenbaum, then shows how they can be applied to obtain new properties of Markov processes by using well-established techniques in Gaussian process theory. This original, readable book will appeal to both researchers and advanced graduate students.

Convergence of Probability Measures
By Patrick Billingsley


Publisher: John Wiley & Sons, Inc.
Number Of Pages:
Publication Date: 1968
ISBN-10 / ASIN: B000OFMIOW
ISBN-13 / EAN:
Binding: Hardcover

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A Matrix Handbook for Statisticians (Wiley Series in Probability and Statistics)
by George A. F. Seber


Publisher: Wiley-Interscience
Number Of Pages: 559
Publication Date: 2007-11-27
ISBN-10 / ASIN: 0471748692
ISBN-13 / EAN: 9780471748694
Binding: Hardcover


Book Description:

A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications

This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized.

A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include:
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Complex matrices
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A wide range of special matrices and their properties
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Special products and operators, such as the Kronecker product
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Partitioned and patterned matrices
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Matrix analysis and approximation
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Matrix optimization
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Majorization
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Random vectors and matrices
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Inequalities, such as probabilistic inequalities

Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

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Statistics for Nuclear and Particle Physicists
by Louis Lyons

Publisher: Cambridge University Press
Number Of Pages: 236
Publication Date: 1986-03-31
ISBN-10 / ASIN: 0521255406
ISBN-13 / EAN: 9780521255400
Binding: Hardcover


Book Description:

Written by a non-statistician for non-statisticians, the book emphasizes the practical approach to those problems in statistics that arise regularly in data analysis situations in nuclear and high energy physics experiments. Rather than concentrate on proofs and theorems, the author provides an abundance of simple examples that illustrate the general ideas presented. This allows the reader to obtain maximum information in the simplest manner. Possible difficulties with the various techniques, and pitfalls to be avoided, are also discussed. This commonsense approach to statistical formalism enables nuclear physicists to better understand how to do justice to their analysis and interpretation of data.



Summary: Do you want your Phd?
Rating: 5

As a high energy physics graduate student, I know of no other book which provides a better grounding in the data analysis techniques needed in an HEP phd. This book has been invaluable to me. It has also been invaluable to many of my professors and friends. If you are doing an HEP phd, you should get this book. Its as simple as that.

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Probability and Statistics in Experimental Physics
by Byron P. Roe

Publisher: Springer
Number Of Pages: 208
Publication Date: 1997-12-05
ISBN-10 / ASIN: 0387978496
ISBN-13 / EAN: 9780387978499
Binding: Hardcover


Book Description:

This book is a practical introduction to the use of probability and statistics in experimental physics for graduate students and advanced undergraduates. It is intended as a practical guide, not as a comprehensive text in probability and statistics. The emphasis is on applications and understanding, on theorems and techniques that are actually used in experimental physics. Proofs of theorems are generally omitted unless they contribute to the intuition in understanding and applying the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to some of the Fortran routines available in the CERN library, but other systems, such as Maple, will also be useful. Topics covered include: basic concepts and definitions; general results, independent of specific distributions; discrete distributions; the normal distribution and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence limits; estimation methods; curve fitting, robustness estimates, and likelihood ratios; interpolating functions and unfolding problems; fitting data with constraints; robust estimation methods.



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Statistical Tables for Biological, Agricultural and Medical Research
by Sir Ronald & Yates, Frank Fisher
Publisher: Oliver & Boyd
Number Of Pages: 148
Publication Date: 1963
ISBN-10 / ASIN: 0050008722
ISBN-13 / EAN: 9780050008720
Binding: Hardcover

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3.255 MB

Measuring Health: A Guide to Rating Scales and Questionnaires, 3rd edition
by Ian McDowell


Publisher: Oxford University Press, USA
Number Of Pages: 768
Publication Date: 2006-03-09
ISBN-10 / ASIN: 0195165675
ISBN-13 / EAN: 9780195165678
Binding: Hardcover


Product Description:

Worldwide economic constraints on health carehealth services research
health systemhealth measurementedition
book provides a critical overview of the field of health measurement, with a technical introduction and discussion of the history and future directions for the field. This latest edition updates
anxiety measurement to accompany the one on depression. It has also added new instruments to those previously reviewed in each of the chapters in the book.LChapters cover measurements of physical disability, social health, psychological well-being, anxiety, depression, mental status testing, pain,
general health status and quality of life. Each chapter presents a tabular comparison of the quality of the instruments reviewed, followed by a detailed description of each method, covering its purpose and conceptual basis, its reliability and validity and, where possible, shows a copy of the
actual scale. To ensure accuracy of the information, each review has been approved by the original author of each instrument or by an acknowledged expert. studies require instruments to monitor the outcomes of care and the output of the systems have highlighted the importance of evidence-based medicine and evidence-based health policy. The resulting clinical trials and , this tools and serves as a guide for choosing among them.LNow in its third . However, the over-abundance of competing measurement scales can make choosing a measure difficult at best. Measuring Health provides in-depth reviews of over 100 of the leading the information on each of the measures previously reviewed, and includes a complete new chapter on



Summary: measuring health: a guide to rating scales and questionnaires
Rating: 5

Great resource. A gold-standard for anyone in the field of health psychology


Summary: For reliability and validity
Rating: 5

In an era of accountability, McDowell and Newell do an excellent job of pulling together instruments to assess patients' health. Although this volume was primary designed for Occupational and Physical Therapists, it should have a broader audience. It includes over 80 instruments with a summary on how to employ each device with estimates of reliability and validity. They give more than adequate details to enable the professional to make decisions regarding the quality and appropriateness of each single measure. Users of these tools need to comprehend the extremegood job explaining the difference between ADL and IADL. lengths that it took for McDowell and Newell to accomplish their task. Their work is truly impressive. On pages 47-50, the authors do a particularly

In addition, the authors do a particularly good job in providing technical details needed by professionals to make decisions about the need and appropriateness of an instrument to serve the specific needs of a patient. Students who are learning about calibration of psychometric instruments will also find the work beneficial. They will immediately see the practical application of theoretical concepts presented in classroom decisions. I have placed this fine book on closed serve for students to use after my presentation on reliability and validity.

Every university library should adopt a copy this is fine monograph.

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Solutions Manual for Statistical Inference 2e
by Casella G., Berger R.L. and Santana D.
2.17MB PDF

Observed Confidence Levels: Theory and Application
by Alan M. Polansky


Publisher: Chapman & Hall/CRC
Number Of Pages: 288
Publication Date: 2007-10-26
ISBN-10 / ASIN: 1584888024
ISBN-13 / EAN: 9781584888024
Binding: Hardcover


Book Description:

Illustrating a simple, novelObserved Confidence Levels: Theory and Application describes the basic development of observed confidence levels, a methodology that can be applied to a variety of common multiple testing problems in statistical inference. It focuses on the modern nonparametric framework of bootstrap-based estimates, allowing for substantial theoretical development and for relatively simple solutions to numerous interesting problems. method for solving an array of statistical problems,

After an introduction, the book develops the theory and applicationvector parameters, and linear models. It then examines nonparametric problems often associated with smoothing methods, including nonparametric density estimation and regression. The author also describes applications in generalized linear models, classical nonparametric statistics, multivariate analysis, and survival analysis as well as compares the method of observed confidence levels to hypothesis testing, multiple comparisons, and Bayesian posterior probabilities. In addition, the appendix presents some background material on the asymptotic expansion theory used in the book. of observed confidence levels for general scalar parameters,

Helping you choose the most reliable method for a variety of problems, this book shows how observed confidence levels provide useful information on the relative truth of hypotheses in multiple testing problems

Statistical Decision Theory and Bayesian Analysis (Springer Series in Statistics)
by James O. Berger


Publisher: Springer
Number Of Pages: 617
Publication Date: 1993-03-25
ISBN-10 / ASIN: 0387960988
ISBN-13 / EAN: 9780387960982
Binding: Hardcover


Book Description:

"The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.



Summary: excellent book by a top Bayesian decision theorist
Rating: 5

Jim Berger is well known for his work in decision theory, Bayesian methods amd his texts on these subjects. This one is certainly one of the best to cover decision theory and give a rigorous treatment to Bayesian methods, particularly in the context of decision theory.


Summary: Absolutely amazing: a unique text presenting theory in a useful way!
Rating: 5

This book (which is becoming somewhat of a classic) is simply outstanding. The author's philosophical and mathematical reasoning is impeccable. This book is very deep and will not just teach you theory and techniques but will teach you how to think and how to approach and formulate problems, as well as how to interpret the results obtained by various methods and use them in a practical setting. This book is very practically oriented. The best thing about this book, however, is that it is so clearly written. Berger is an outstanding writer with the ability to communicate difficult concepts without watering them down.

This book covers decision theory and Bayesian statistics in much depth. While it is a high-level text oriented towards researchers and people with strong backgrounds, it is clear enough that someone learning this material for the first time would have little trouble with it. It provides ample review and clear exposition of key mathematical and statistical concepts such as sufficiency, convexity. Its exposition of invariance (with respect to groups of transformations) is both the clearest and most rigorous I have found in any statistics text. In my opinion, there are no weak or unclear sections in the book, and the difficulty level does not rise disproportionately in later chapters the way it does in many books on similar subjects.

This book is rich with examples, and the examples are mostly of a practical nature, in contrast to the "toy" mathematical examples that dominate many books written at this advanced level. The exercises are diverse and extensive, and have a good gradient of difficult level for building both technical skill and depth of understanding. The exercises are more carefully worded and constructed than is typical for books at this level. Most of the typos have been caught and corrected in the revised edition.

This is an old book. The author, in his philosophy, was arguably well ahead of his time. The ideas contained in this book are highly modern. However, the use of computers in statistics has changed since this book was written. This book is a book on theory and will teach you how to do things by hand. I do not see this as a weakness at all, but one should be aware of it when considering this book. But, as the other author noted, it will not teach you algorithms, numerical techniques, or how to use a statistical computing package.

I think this book would make an outstanding textbook for a course in statistical decision theory or Bayesian statistics. It would also be useful as a supplement for a course in statistical inference. Perhaps more importantly, it is very useful for self-study. I think this book would make an excellent addition to any statistician's collection--and it would certainly be useful to people working in more practical settings, such as business, science, or social science. If you are going to buy any one advanced, theoretical book on statistics, this would be the one to buy.


Summary: Excellent book on Bayesian analysis
Rating: 5

[1] It is a classical book written by an excellent mathematician, not a worker of statistics!
[2] Its mathematics is precise and fascinating.
[3] The philosophy of Bayesian statistics is well discussed.
[4] It's worthy to read it many times.
[5] At the time of its publication, the revolutionary computational statistics was still in gestation. So, it is unfair to criticize its lack of numerical simulation, etc. As a comlement, some pragmatistic books are recommended, such as J. Liu's book on MCMC methods, Tanner's Tools for Statistical Inference, etc.


Summary: Excellent book!!!
Rating: 5

This book is awesome. This book is theoretical but it has enough examples to follow along. The author's presentation is clear in every step. The problems in the book are challenging but do-able. Don't need another reference book.


Summary: a very readable and useful book
Rating: 5

The professor used this book in the math stat course I took 2 years ago. I did not like the book at first, it looks too long to be covered. but it turned to be very easy to follow (You still need to think, but the author, being a hero in this field, made a very clear presentation to the audience). As long as you invest some time and brain, you can get a lot from this book. The problems are very good and instructional too.

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Leonard Eugene Dickson, "Linear Groups with an Exposition of Galois Field Theory"
Dover Publications | 2003-09-18 | ISBN: 0486495485 | 336 pages | Djvu | 13,6 Mb

Hailed as a milestone in the development of modern algebra, this classic exposition of the theory of groups is well within the range of graduate students. Its particular value lies in its attention to practical applications: the theory of the solvability of equations, theory of differential equations, complex number systems, and the foundations of geometry, where Euclidean or parabolic geometry, elliptic geometry, and hyperbolic geometry can be completely characterized by groups. The first of the two-part treatment consists of an extensive presentation of the theory of Galois Fields, with a wealth of examples and theorems; the second part features a discussion of linear groups in a Galois Field, with a survey of the known simple groups of finite composite order.