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| pitman probability: Probability Jim Pitman, 1999-05-21 Preface to the Instructor This is a text for a one-quarter or one-semester course in probability, aimed at stu dents who have done a year of calculus. The book is organized so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail. It is not possible to go through all these examples in class. Rather, I suggest that you deal quickly with the main points of theory, then spend class time on problems from the exercises, or your own favorite problems. The most valuable thing for students to learn from a course like this is how to pick up a probability problem in a new setting and relate it to the standard body of theory. The more they see this happen in class, and the more they do it themselves in exercises, the better. The style of the text is deliberately informal. My experience is that students learn more from intuitive explanations, diagrams, and examples than they do from theo rems and proofs. So the emphasis is on problem solving rather than theory. |
| pitman probability: Combinatorial Stochastic Processes Jim Pitman, 2006-05-11 The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes. |
| pitman probability: Some Basic Theory for Statistical Inference E.J.G. Pitman, 2018-01-18 In this book the author presents with elegance and precision some of the basic mathematical theory required for statistical inference at a level which will make it readable by most students of statistics. |
| pitman probability: Probability Rick Durrett, 2010-08-30 This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject. |
| pitman probability: Measure, Integral and Probability Marek Capinski, (Peter) Ekkehard Kopp, 2013-06-29 The central concepts in this book are Lebesgue measure and the Lebesgue integral. Their role as standard fare in UK undergraduate mathematics courses is not wholly secure; yet they provide the principal model for the development of the abstract measure spaces which underpin modern probability theory, while the Lebesgue function spaces remain the main sour ce of examples on which to test the methods of functional analysis and its many applications, such as Fourier analysis and the theory of partial differential equations. It follows that not only budding analysts have need of a clear understanding of the construction and properties of measures and integrals, but also that those who wish to contribute seriously to the applications of analytical methods in a wide variety of areas of mathematics, physics, electronics, engineering and, most recently, finance, need to study the underlying theory with some care. We have found remarkably few texts in the current literature which aim explicitly to provide for these needs, at a level accessible to current under graduates. There are many good books on modern prob ability theory, and increasingly they recognize the need for a strong grounding in the tools we develop in this book, but all too often the treatment is either too advanced for an undergraduate audience or else somewhat perfunctory. |
| pitman probability: Introduction to Probability David F. Anderson, Timo Seppäläinen, Benedek Valkó, 2017-11-02 This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work. |
| pitman probability: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| pitman probability: Pitman's Measure of Closeness Jerome P. Keating, Robert L. Mason, Pranab K. Sen, 1993-01-01 This book provides a thorough introduction to the methods and known results associated with PMC. |
| pitman probability: Modern Probability Theory and Its Applications Emanuel Parzen, 1960 |
| pitman probability: Probability Theory , 2013 Probability theory |
| pitman probability: Probability for Statisticians Galen R. Shorack, 2006-05-02 The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales. |
| pitman probability: Probability and Real Trees Steven N. Evans, 2007-09-26 Random trees and tree-valued stochastic processes are of particular importance in many fields. Using the framework of abstract tree-like metric spaces and ideas from metric geometry, Evans and his collaborators have recently pioneered an approach to studying the asymptotic behavior of such objects when the number of vertices goes to infinity. This publication surveys the relevant mathematical background and present some selected applications of the theory. |
| pitman probability: Pitman's Measure of Closeness Jerome P. Keating, Robert L. Mason, Pranab K. Sen, 1993-01-01 This book provides a thorough introduction to the methods and known results associated with PMC. |
| pitman probability: Elementary Probability for Applications Rick Durrett, 2009-07-31 This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management. |
| pitman probability: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. |
| pitman probability: Itô’s Stochastic Calculus and Probability Theory Nobuyuki Ikeda, Sinzo Watanabe, Masatoshi Fukushima, Hiroshi Kunita, 2012-12-06 Professor Kiyosi Ito is well known as the creator of the modern theory of stochastic analysis. Although Ito first proposed his theory, now known as Ito's stochastic analysis or Ito's stochastic calculus, about fifty years ago, its value in both pure and applied mathematics is becoming greater and greater. For almost all modern theories at the forefront of probability and related fields, Ito's analysis is indispensable as an essential instrument, and it will remain so in the future. For example, a basic formula, called the Ito formula, is well known and widely used in fields as diverse as physics and economics. This volume contains 27 papers written by world-renowned probability theorists. Their subjects vary widely and they present new results and ideas in the fields where stochastic analysis plays an important role. Also included are several expository articles by well-known experts surveying recent developments. Not only mathematicians but also physicists, biologists, economists and researchers in other fields who are interested in the effectiveness of stochastic theory will find valuable suggestions for their research. In addition, students who are beginning their study and research in stochastic analysis and related fields will find instructive and useful guidance here. This volume is dedicated to Professor Ito on the occasion of his eightieth birthday as a token of deep appreciation for his great achievements and contributions. An introduction to and commentary on the scientific works of Professor Ito are also included. |
| pitman probability: Probability and Statistics for Computer Scientists Michael Baron, 2013-08-05 Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling ToolsIncorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make o |
| pitman probability: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap. |
| pitman probability: A First Course in Probability Tapas K. Chandra, Dipak Chatterjee, 2001 Examples, both solved and unsolved, have been drawn from all walks of life to convince readers about the ethereal existence of probability and to familiarize them with the techniques of solving a variety of similar problems.. |
| pitman probability: Noah's Flood William Ryan, Walter Pitman, 1998 Basing their research on geophysics, oral legends, and archaeology, the authors offer evidence that the flood in the book of Genesis actually occurred. |
| pitman probability: Probability Theory: STAT310/MATH230 Amir Dembo, 2014-10-24 Probability Theory: STAT310/MATH230By Amir Dembo |
| pitman probability: Probability and Statistical Physics in Two and More Dimensions Clay Mathematics Institute. Summer School, 2012 This volume is a collection of lecture notes for six of the ten courses given in Buzios, Brazil by prominent probabilists at the 2010 Clay Mathematics Institute Summer School, ``Probability and Statistical Physics in Two and More Dimensions'' and at the XIV Brazilian School of Probability. In the past ten to fifteen years, various areas of probability theory related to statistical physics, disordered systems and combinatorics have undergone intensive development. A number of these developments deal with two-dimensional random structures at their critical points, and provide new tools and ways of coping with at least some of the limitations of Conformal Field Theory that had been so successfully developed in the theoretical physics community to understand phase transitions of two-dimensional systems. Included in this selection are detailed accounts of all three foundational courses presented at the Clay school--Schramm-Loewner Evolution and other Conformally Invariant Objects, Noise Sensitivity and Percolation, Scaling Limits of Random Trees and Planar Maps--together with contributions on Fractal and Multifractal properties of SLE and Conformal Invariance of Lattice Models. Finally, the volume concludes with extended articles based on the courses on Random Polymers and Self-Avoiding Walks given at the Brazilian School of Probability during the final week of the school. Together, these notes provide a panoramic, state-of-the-art view of probability theory areas related to statistical physics, disordered systems and combinatorics. Like the lectures themselves, they are oriented towards advanced students and postdocs, but experts should also find much of interest. |
| pitman probability: Classic Topics on the History of Modern Mathematical Statistics Prakash Gorroochurn, 2016-03-29 There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent. —George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200-year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses post-Fisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of Neyman–Pearson theory, which includes a discussion of the differences to Fisher’s works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference. |
| pitman probability: Probability and Statistical Inference Robert V. Hogg, Elliot A. Tanis, 1988 This user-friendly introduction to the mathematics of probability and statistics (for readers with a background in calculus) uses numerous applications--drawn from biology, education, economics, engineering, environmental studies, exercise science, health science, manufacturing, opinion polls, psychology, sociology, and sports--to help explain and motivate the concepts. A review of selected mathematical techniques is included, and an accompanying CD-ROM contains many of the figures (many animated), and the data included in the examples and exercises (stored in both Minitab compatible format and ASCII). Empirical and Probability Distributions. Probability. Discrete Distributions. Continuous Distributions. Multivariable Distributions. Sampling Distribution Theory. Importance of Understanding Variability. Estimation. Tests of Statistical Hypotheses. Theory of Statistical Inference. Quality Improvement Through Statistical Methods. For anyone interested in the Mathematics of Probability and Statistics. |
| pitman probability: Bayesian Theory José M. Bernardo, Adrian F. M. Smith, 2009-09-25 This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging critical re-examination of controversial issues. The level of mathematics used is such that most material is accessible to readers with knowledge of advanced calculus. In particular, no knowledge of abstract measure theory is assumed, and the emphasis throughout is on statistical concepts rather than rigorous mathematics. The book will be an ideal source for all students and researchers in statistics, mathematics, decision analysis, economic and business studies, and all branches of science and engineering, who wish to further their understanding of Bayesian statistics |
| pitman probability: Probability with Martingales David Williams, 1991-02-14 This is a masterly introduction to the modern, and rigorous, theory of probability. The author emphasises martingales and develops all the necessary measure theory. |
| pitman probability: Plane Answers to Complex Questions Ronald Christensen, 2013-03-09 The third edition of Plane Answers includes fundamental changes in how some aspects of the theory are handled. Chapter 1 includes a new section that introduces generalized linear models. Primarily, this provides a defini tion so as to allow comments on how aspects of linear model theory extend to generalized linear models. For years I have been unhappy with the concept of estimability. Just because you cannot get a linear unbiased estimate of something does not mean you cannot estimate it. For example, it is obvious how to estimate the ratio of two contrasts in an ANOVA, just estimate each one and take their ratio. The real issue is that if the model matrix X is not of full rank, the parameters are not identifiable. Section 2.1 now introduces the concept of identifiability and treats estimability as a special case of identifiability. This change also resulted in some minor changes in Section 2.2. In the second edition, Appendix F presented an alternative approach to dealing with linear parametric constraints. In this edition I have used the new approach in Section 3.3. I think that both the new approach and the old approach have virtues, so I have left a fair amount of the old approach intact. Chapter 8 contains a new section with a theoretical discussion of models for factorial treatment structures and the introduction of special models for homologous factors. This is closely related to the changes in Section 3.3. |
| pitman probability: Applying and Interpreting Statistics Glen McPherson, 2013-06-29 In the period since the first edition was published, I have appreciated the corre spondence from all parts of the world expressing thanks for the presentation of statistics from a user's perspective. It has been particularIy pleasing to have been invited to contribute to course restructuring and development based on the ap proach to learning and applying statistics that underlies this book. In addition, I have taken account of suggestions and criticisms, and I hope that this new edition will address all major concerns. The range of readily accessible statistical methods has greatly expanded over the past decade, particularly with the growing accessibility of comprehensive statisti cal computing packages. The approach adopted in this book has anticipated the changes by its emphasis on building understanding and skills in method selection and interpretation of findings. There has been a reduction in computational for mulas to reflect the fact that basic statistical analyses are now almost universally undertaken on computers. This has allowed the inclusion of a more general cover age of unifying methodology, particularly Generalized linear methodology, which permits users to more accurately match their requirements to statistical models and methods. A major addition is a chapter on the commonly used multivariate methods. |
| pitman probability: Regression Analysis Ashish Sen, Muni Srivastava, 2012-12-06 Any method of fitting equations to data may be called regression. Such equations are valuable for at least two purposes: making predictions and judging the strength of relationships. Because they provide a way of em pirically identifying how a variable is affected by other variables, regression methods have become essential in a wide range of fields, including the social sciences, engineering, medical research and business. Of the various methods of performing regression, least squares is the most widely used. In fact, linear least squares regression is by far the most widely used of any statistical technique. Although nonlinear least squares is covered in an appendix, this book is mainly about linear least squares applied to fit a single equation (as opposed to a system of equations). The writing of this book started in 1982. Since then, various drafts have been used at the University of Toronto for teaching a semester-long course to juniors, seniors and graduate students in a number of fields, including statistics, pharmacology, engineering, economics, forestry and the behav ioral sciences. Parts of the book have also been used in a quarter-long course given to Master's and Ph.D. students in public administration, urban plan ning and engineering at the University of Illinois at Chicago (UIC). This experience and the comments and criticisms from students helped forge the final version. |
| pitman probability: Testing Statistical Hypotheses Erich L. Lehmann, Joseph P. Romano, 2006-03-30 The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760. |
| pitman probability: Statistics and Finance David Ruppert, 2014-02-26 This textbook emphasizes the applications of statistics and probability to finance. Students are assumed to have had a prior course in statistics, but no background in finance or economics. The basics of probability and statistics are reviewed and more advanced topics in statistics, such as regression, ARMA and GARCH models, the bootstrap, and nonparametric regression using splines, are introduced as needed. The book covers the classical methods of finance such as portfolio theory, CAPM, and the Black-Scholes formula, and it introduces the somewhat newer area of behavioral finance. Applications and use of MATLAB and SAS software are stressed. The book will serve as a text in courses aimed at advanced undergraduates and masters students in statistics, engineering, and applied mathematics as well as quantitatively oriented MBA students. Those in the finance industry wishing to know more statistics could also use it for self-study. |
| pitman probability: Introduction to Graphical Modelling David Edwards, 2012-12-06 Graphic modelling is a form of multivariate analysis that uses graphs to represent models. These graphs display the structure of dependencies, both associational and causal, between the variables in the model. This textbook provides an introduction to graphical modelling with emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, a freeware version of which can be downloaded from the Internet. Following an introductory chapter which sets the scene and describes some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to the second edition. Chapter 7 describes the use of directed graphs, chain graphs, and other graphs. Chapter 8 summarizes some recent work on causal inference, relevant when graphical models are given a causal interpretation. This book will provide a useful introduction to this topic for students and researchers. |
| pitman probability: Statistical Methods for the Analysis of Repeated Measurements Charles S. Davis, 2008-01-10 A comprehensive introduction to a wide variety of statistical methods for the analysis of repeated measurements. It is designed to be both a useful reference for practitioners and a textbook for a graduate-level course focused on methods for the analysis of repeated measurements. The important features of this book include a comprehensive coverage of classical and recent methods for continuous and categorical outcome variables; numerous homework problems at the end of each chapter; and the extensive use of real data sets in examples and homework problems. |
| pitman probability: Theory of Point Estimation Erich L. Lehmann, George Casella, 2006-05-02 Since the publication in 1983 of Theory of Point Estimation, much new work has made it desirable to bring out a second edition. The inclusion of the new material has increased the length of the book from 500 to 600 pages; of the approximately 1000 references about 25% have appeared since 1983. The greatest change has been the addition to the sparse treatment of Bayesian inference in the first edition. This includes the addition of new sections on Equivariant, Hierarchical, and Empirical Bayes, and on their comparisons. Other major additions deal with new developments concerning the information in equality and simultaneous and shrinkage estimation. The Notes at the end of each chapter now provide not only bibliographic and historical material but also introductions to recent development in point estimation and other related topics which, for space reasons, it was not possible to include in the main text. The problem sections also have been greatly expanded. On the other hand, to save space most of the discussion in the first edition on robust estimation (in particu lar L, M, and R estimators) has been deleted. This topic is the subject of two excellent books by Hampel et al (1986) and Staudte and Sheather (1990). Other than subject matter changes, there have been some minor modifications in the presentation. |
| pitman probability: Elements of Large-Sample Theory E.L. Lehmann, 2006-04-18 Elements of Large-Sample Theory provides a unified treatment of first- order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level and is suitable for students at the master's level in statistics and in aplied fields who have a background of two years of calculus. E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: Lehmann/Casella, Theory at Point Estimation, 2nd ed. Springer-Verlag New York, Inc., 1998, ISBN 0- 387-98502-6 Lehmann, Testing Statistical Hypotheses, 2nd ed. Springer-Verlag New York, Inc., 1997, ISBN 0-387-94919-4 |
| pitman probability: Optimization Kenneth Lange, 2013-03-09 Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students’ skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on convexity serves as bridge between linear and nonlinear programming and makes it possible to give a modern exposition of linear programming based on the interior point method rather than the simplex method. The emphasis on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes graduate students in applied mathematics, computational biology, computer science, economics, and physics as well as upper division undergraduate majors in mathematics who want to see rigorous mathematics combined with real applications. Chapter 1 reviews classical methods for the exact solution of optimization problems. Chapters 2 and 3 summarize relevant concepts from mathematical analysis. Chapter 4 presents the Karush-Kuhn-Tucker conditions for optimal points in constrained nonlinear programming. Chapter 5 discusses convexity and its implications in optimization. Chapters 6 and 7 introduce the MM and the EM algorithms widely used in statistics. Chapters 8 and 9 discuss Newton’s method and its offshoots, quasi-Newton algorithms and the method of conjugate gradients. Chapter 10 summarizes convergence results, and Chapter 11 briefly surveys convex programming, duality, and Dykstra’s algorithm. From the reviews: ...An excellent, imaginative, and authoritative text on the difficult topic of modeling the problems of multivariate outcomes with different scaling levels, different units of analysis, and differentstudy designs simultaneously. Biometrics, March 2005 ...As a textbook, Optimization does provide a valuable introduction to an important branch of applicable mathematics. Technometrics, August 2005 ...I found Optimization to be an extremely engaging textbook....the text is ideal for graduate students or researchers beginning research on optimization problems in statistics. There is little doubt that someone who worked through the text as part of a reading course or specialized graduate seminar would benefit greatly from the author's perspective... Journal of the American Statistical Association, December 2005 |
| pitman probability: Mathematical Statistics Jun Shao, 2008-02-03 This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results. In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics. Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, conditional independence, Markov chains, martingales, Edgeworth and Cornish-Fisher expansions, and proofs to many key theorems such as the dominated convergence theorem, monotone convergence theorem, uniqueness theorem, continuity theorem, law of large numbers, and central limit theorem. A new section in Chapter 5 introduces semiparametric models, and a number of new exercises were added to each chapter. |
| pitman probability: Seminaire de Probabilites XXXI Jacques Azema, Michel Emery, Marc Yor, 2008-05-01 The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures. |
| pitman probability: A Chronicle of Permutation Statistical Methods Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke Jr., 2014-04-11 The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A non-mathematical approach makes the text accessible to readers of all levels. |
| pitman probability: Permutation Statistical Methods with R Kenneth J. Berry, Kenneth L. Kvamme, Janis E. Johnston, Paul W. Mielke, Jr., 2021-09-27 This book takes a unique approach to explaining permutation statistics by integrating permutation statistical methods with a wide range of classical statistical methods and associated R programs. It opens by comparing and contrasting two models of statistical inference: the classical population model espoused by J. Neyman and E.S. Pearson and the permutation model first introduced by R.A. Fisher and E.J.G. Pitman. Numerous comparisons of permutation and classical statistical methods are presented, supplemented with a variety of R scripts for ease of computation. The text follows the general outline of an introductory textbook in statistics with chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, completely-randomized analysis of variance, randomized-blocks analysis of variance, simple linear regression and correlation, and the analysis of goodness of fit and contingency. Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity, depend only on the observed data, and do not require random sampling. The methods are relatively new in that it took modern computing power to make them available to those working in mainstream research. Designed for an audience with a limited statistical background, the book can easily serve as a textbook for undergraduate or graduate courses in statistics, psychology, economics, political science or biology. No statistical training beyond a first course in statistics is required, but some knowledge of, or some interest in, the R programming language is assumed. |
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Welcome to Borough of Pitman, NJ
Welcome to the Borough of Pitman, learn about our neighborhoods, schools, community services, shopping and dining.
Pitman
See what makes Pitman the nation’s leading distributor of freshwater tackle. We provide our dealers with leading edge products and proven favorites.
Pitman Funeral Home | Wentzville MO funeral home a…
Mar 19, 2025 · Founded in 1922, Pitman Funeral Home continues to be owned and operated by the Pitman family. With locations in Wentzville, …
MyPitman | Login Portal - Pitman Training
Your gateway to Pitman Training courses and resources. When you begin training, you’ll receive access to myPitman, our advanced online …
Pitman, New Jersey - Wikipedia
Pitman is a borough in Gloucester County, in the U.S. state of New Jersey. As of the 2020 United States census, the borough's population was 8,780, …
