Models For Probability And Statistical Inference Download Ebook PDF Epub Online

Author : James H. Stapleton
Publisher : John Wiley & Sons
Release : 2007-12-14
Page : 512
Category : Mathematics
ISBN 13 : 9780470183403
Description :


This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.


Author : Miltiadis C. Mavrakakis
Jeremy Penzer
Publisher : CRC Press
Release : 2021-03-29
Page : 444
Category : Mathematics
ISBN 13 : 131536204X
Description :


Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting. Features: •Complete introduction to mathematical probability, random variables, and distribution theory. •Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes. •Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference. •Detailed introduction to Bayesian statistics and associated topics. •Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC). This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.


Author : J.G. Kalbfleisch
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 343
Category : Mathematics
ISBN 13 : 1461210968
Description :


A carefully written text, suitable as an introductory course for second or third year students. The main scope of the text guides students towards a critical understanding and handling of data sets together with the ensuing testing of hypotheses. This approach distinguishes it from many other texts using statistical decision theory as their underlying philosophy. This volume covers concepts from probability theory, backed by numerous problems with selected answers.


Author : Aris Spanos
Publisher : Cambridge University Press
Release : 2019-08-31
Page : 846
Category : Business & Economics
ISBN 13 : 1107185149
Description :


This empirical research methods course enables informed implementation of statistical procedures, giving rise to trustworthy evidence.


Author : Robert V. Hogg
Elliot A. Tanis
Publisher :
Release : 1977
Page : 450
Category : Mathematical statistics
ISBN 13 :
Description :


Probability; Distributions of the discrete type; Empirical distributions; Distributions of the continuous type; Basic sampling distribution theory; Distribution - free confidence intervals; Estimation with normal models; Tests of statistical hypotheses; Multivariate distributions; Chi - square tests of models; Analysis of variance; A brief theory of statistical inference.


Author : Robert Bartoszynski
Magdalena Niewiadomska-Bugaj
Publisher : John Wiley & Sons
Release : 2007-11-16
Page : 672
Category : Mathematics
ISBN 13 : 9780470191583
Description :


Now updated in a valuable new edition—this user-friendly book focuses on understanding the "why" of mathematical statistics Probability and Statistical Inference, Second Edition introduces key probability and statis-tical concepts through non-trivial, real-world examples and promotes the developmentof intuition rather than simple application. With its coverage of the recent advancements in computer-intensive methods, this update successfully provides the comp-rehensive tools needed to develop a broad understanding of the theory of statisticsand its probabilistic foundations. This outstanding new edition continues to encouragereaders to recognize and fully understand the why, not just the how, behind the concepts,theorems, and methods of statistics. Clear explanations are presented and appliedto various examples that help to impart a deeper understanding of theorems and methods—from fundamental statistical concepts to computational details. Additional features of this Second Edition include: A new chapter on random samples Coverage of computer-intensive techniques in statistical inference featuring Monte Carlo and resampling methods, such as bootstrap and permutation tests, bootstrap confidence intervals with supporting R codes, and additional examples available via the book's FTP site Treatment of survival and hazard function, methods of obtaining estimators, and Bayes estimating Real-world examples that illuminate presented concepts Exercises at the end of each section Providing a straightforward, contemporary approach to modern-day statistical applications, Probability and Statistical Inference, Second Edition is an ideal text for advanced undergraduate- and graduate-level courses in probability and statistical inference. It also serves as a valuable reference for practitioners in any discipline who wish to gain further insight into the latest statistical tools.


Author : Steven J. Janke
Frederick Tinsley
Publisher : John Wiley & Sons
Release : 2005-09-15
Page : 576
Category : Mathematics
ISBN 13 : 0471740101
Description :


A multidisciplinary approach that emphasizes learning by analyzingreal-world data sets This book is the result of the authors' hands-on classroomexperience and is tailored to reflect how students best learn toanalyze linear relationships. The text begins with the introductionof four simple examples of actual data sets. These examples aredeveloped and analyzed throughout the text, and more complicatedexamples of data sets are introduced along the way. Taking amultidisciplinary approach, the book traces the conclusion of theanalyses of data sets taken from geology, biology, economics,psychology, education, sociology, and environmental science. As students learn to analyze the data sets, they masterincreasingly sophisticated linear modeling techniques,including: * Simple linear models * Multivariate models * Model building * Analysis of variance (ANOVA) * Analysis of covariance (ANCOVA) * Logistic regression * Total least squares The basics of statistical analysis are developed and emphasized,particularly in testing the assumptions and drawing inferences fromlinear models. Exercises are included at the end of each chapter totest students' skills before moving on to more advanced techniquesand models. These exercises are marked to indicate whethercalculus, linear algebra, or computer skills are needed. Unlike other texts in the field, the mathematics underlying themodels is carefully explained and accessible to students who maynot have any background in calculus or linear algebra. Mostchapters include an optional final section on linear algebra forstudents interested in developing a deeper understanding. The many data sets that appear in the text are available on thebook's Web site. The MINITAB(r) software program is used toillustrate many of the examples. For students unfamiliar withMINITAB(r), an appendix introduces the key features needed to studylinear models. With its multidisciplinary approach and use of real-world data setsthat bring the subject alive, this is an excellent introduction tolinear models for students in any of the natural or socialsciences.


Author : Sean Gailmard
Publisher : Cambridge University Press
Release : 2014-06-09
Page : 388
Category : Business & Economics
ISBN 13 : 1107003148
Description :


Written specifically for graduate students and practitioners beginning social science research, Statistical Modeling and Inference for Social Science covers the essential statistical tools, models and theories that make up the social scientist's toolkit. Assuming no prior knowledge of statistics, this textbook introduces students to probability theory, statistical inference and statistical modeling, and emphasizes the connection between statistical procedures and social science theory. Sean Gailmard develops core statistical theory as a set of tools to model and assess relationships between variables - the primary aim of social scientists - and demonstrates the ways in which social scientists express and test substantive theoretical arguments in various models. Chapter exercises guide students in applying concepts to data, extending their grasp of core theoretical concepts. Students gain the ability to create, read and critique statistical applications in their fields of interest.


Author : George G. Roussas
Publisher : Academic Press
Release : 2014-10-21
Page : 624
Category : Mathematics
ISBN 13 : 0128004371
Description :


An Introduction to Probability and Statistical Inference, Second Edition, guides you through probability models and statistical methods and helps you to think critically about various concepts. Written by award-winning author George Roussas, this book introduces readers with no prior knowledge in probability or statistics to a thinking process to help them obtain the best solution to a posed question or situation. It provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. This text contains an enhanced number of exercises and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities. Reorganized material is included in the statistical portion of the book to ensure continuity and enhance understanding. Each section includes relevant proofs where appropriate, followed by exercises with useful clues to their solutions. Furthermore, there are brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises are available to instructors in an Answers Manual. This text will appeal to advanced undergraduate and graduate students, as well as researchers and practitioners in engineering, business, social sciences or agriculture. Content, examples, an enhanced number of exercises, and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities Reorganized material in the statistical portion of the book to ensure continuity and enhance understanding A relatively rigorous, yet accessible and always within the prescribed prerequisites, mathematical discussion of probability theory and statistical inference important to students in a broad variety of disciplines Relevant proofs where appropriate in each section, followed by exercises with useful clues to their solutions Brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises available to instructors in an Answers Manual


Author : Alan Agresti
Publisher : John Wiley & Sons
Release : 2015-02-23
Page : 480
Category : Mathematics
ISBN 13 : 1118730038
Description :


A valuable overview of the most important ideas and results in statistical modeling Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linearstatistical models. The book presents a broad, in-depth overview of the most commonly usedstatistical models by discussing the theory underlying the models, R software applications,and examples with crafted models to elucidate key ideas and promote practical modelbuilding. The book begins by illustrating the fundamentals of linear models, such as how the model-fitting projects the data onto a model vector subspace and how orthogonal decompositions of the data yield information about the effects of explanatory variables. Subsequently, the book covers the most popular generalized linear models, which include binomial and multinomial logistic regression for categorical data, and Poisson and negative binomial loglinear models for count data. Focusing on the theoretical underpinnings of these models, Foundations ofLinear and Generalized Linear Models also features: An introduction to quasi-likelihood methods that require weaker distributional assumptions, such as generalized estimating equation methods An overview of linear mixed models and generalized linear mixed models with random effects for clustered correlated data, Bayesian modeling, and extensions to handle problematic cases such as high dimensional problems Numerous examples that use R software for all text data analyses More than 400 exercises for readers to practice and extend the theory, methods, and data analysis A supplementary website with datasets for the examples and exercises An invaluable textbook for upper-undergraduate and graduate-level students in statistics and biostatistics courses, Foundations of Linear and Generalized Linear Models is also an excellent reference for practicing statisticians and biostatisticians, as well as anyone who is interested in learning about the most important statistical models for analyzing data.


Author : Jeanne Kowalski
Xin M. Tu
Publisher : John Wiley & Sons
Release : 2008-01-28
Page : 352
Category : Mathematics
ISBN 13 : 9780470186459
Description :


A timely and applied approach to the newly discovered methods and applications of U-statistics Built on years of collaborative research and academic experience, Modern Applied U-Statistics successfully presents a thorough introduction to the theory of U-statistics using in-depth examples and applications that address contemporary areas of study including biomedical and psychosocial research. Utilizing a "learn by example" approach, this book provides an accessible, yet in-depth, treatment of U-statistics, as well as addresses key concepts in asymptotic theory by integrating translational and cross-disciplinary research. The authors begin with an introduction of the essential and theoretical foundations of U-statistics such as the notion of convergence in probability and distribution, basic convergence results, stochastic Os, inference theory, generalized estimating equations, as well as the definition and asymptotic properties of U-statistics. With an emphasis on nonparametric applications when and where applicable, the authors then build upon this established foundation in order to equip readers with the knowledge needed to understand the modern-day extensions of U-statistics that are explored in subsequent chapters. Additional topical coverage includes: Longitudinal data modeling with missing data Parametric and distribution-free mixed-effect and structural equation models A new multi-response based regression framework for non-parametric statistics such as the product moment correlation, Kendall's tau, and Mann-Whitney-Wilcoxon rank tests A new class of U-statistic-based estimating equations (UBEE) for dependent responses Motivating examples, in-depth illustrations of statistical and model-building concepts, and an extensive discussion of longitudinal study designs strengthen the real-world utility and comprehension of this book. An accompanying Web site features SAS? and S-Plus? program codes, software applications, and additional study data. Modern Applied U-Statistics accommodates second- and third-year students of biostatistics at the graduate level and also serves as an excellent self-study for practitioners in the fields of bioinformatics and psychosocial research.


Author : Larry Wasserman
Publisher : Springer Science & Business Media
Release : 2013-12-11
Page : 442
Category : Mathematics
ISBN 13 : 0387217363
Description :


Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.


Author : Jesper Moller
Rasmus Plenge Waagepetersen
Publisher : CRC Press
Release : 2003-09-25
Page : 320
Category : Mathematics
ISBN 13 : 9780203496930
Description :


Spatial point processes play a fundamental role in spatial statistics and today they are an active area of research with many new applications. Although other published works address different aspects of spatial point processes, most of the classical literature deals only with nonparametric methods, and a thorough treatment of the theory and applications of simulation-based inference is difficult to find. Written by researchers at the top of the field, this book collects and unifies recent theoretical advances and examples of applications. The authors examine Markov chain Monte Carlo algorithms and explore one of the most important recent developments in MCMC: perfect simulation procedures.


Author : Ronald Christensen
Publisher : Springer Science & Business Media
Release : 1991
Page : 317
Category : Mathematics
ISBN 13 : 038797413X
Description :


A companion volume to Plane answers to complex questions: the theory of linear models (1987), presenting six chapters with shallow treatments of very broad topics showing how the properties of three fundamental ideas from standard linear model theory can be used to examine multivariate, time series,


Author : Miltiadis C. Mavrakakis
Jeremy Penzer
Publisher : Chapman and Hall/CRC
Release : 2014-12-15
Page : 608
Category : Mathematics
ISBN 13 : 9781584889397
Description :


Modelling, Inference and Data Analysis brings together key topics in mathematical statistics and presents them in a rigorous yet accessible manner. It covers aspects of probability, distribution theory and random processes that are fundamental to a proper understanding of inference. The book also discusses the properties of estimators constructed from a random sample of ends, with sections on methods for estimating parameters in time series models and computationally intensive inferential techniques. The text challenges and excites the more mathematically able students while providing an approachable explanation of advanced statistical concepts for students who struggle with existing texts.


Author : Charles S. Davis
Publisher : Springer Science & Business Media
Release : 2008-01-10
Page : 416
Category : Mathematics
ISBN 13 : 0387215735
Description :


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.


Author : J.G. Kalbfleisch
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page :
Category : Mathematics
ISBN 13 : 1468400916
Description :



Author : Michael J. Evans
Jeffrey S. Rosenthal
Publisher : WH Freeman
Release : 2010-03-01
Page : 200
Category : Mathematics
ISBN 13 : 9781429224635
Description :


Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor to the course, incorporating the computer and offering an integrated approach to inference that includes the frequency approach and the Bayesian inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout. Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. The new edition includes a number of features designed to make the material more accessible and level-appropriate to the students taking this course today.


Author : James H.C. Creighton
Publisher : Springer Science & Business Media
Release : 2012-12-06
Page : 719
Category : Mathematics
ISBN 13 : 1441985409
Description :


Welcome to new territory: A course in probability models and statistical inference. The concept of probability is not new to you of course. You've encountered it since childhood in games of chance-card games, for example, or games with dice or coins. And you know about the "90% chance of rain" from weather reports. But once you get beyond simple expressions of probability into more subtle analysis, it's new territory. And very foreign territory it is. You must have encountered reports of statistical results in voter sur veys, opinion polls, and other such studies, but how are conclusions from those studies obtained? How can you interview just a few voters the day before an election and still determine fairly closely how HUN DREDS of THOUSANDS of voters will vote? That's statistics. You'll find it very interesting during this first course to see how a properly designed statistical study can achieve so much knowledge from such drastically incomplete information. It really is possible-statistics works! But HOW does it work? By the end of this course you'll have understood that and much more. Welcome to the enchanted forest.


Author : Jim Albert
Jingchen Hu
Publisher : CRC Press
Release : 2019-12-19
Page : 538
Category : Mathematics
ISBN 13 : 1351030124
Description :


Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book.