Chapman & Hall/CRC Texts in Statistical Science – serie

Winner of the 2023 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work.The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.FeaturesIntegrates working code into the main text. Illustrates concepts through worked data analysis examples. Emphasizes understanding assumptions and how assumptions are reflected in code. Offers more detailed explanations of the mathematics in optional sections. Presents examples of using the dagitty R package to analyze causal graphs. Provides the rethinking R package on the author's website and on GitHub.

Engineers are expected to design structures and machines that can operate in challenging and volatile environments, while allowing for variation in materials and noise in measurements and signals. Statistics in Engineering, Second Edition: With Examples in MATLAB and R covers the fundamentals of probability and statistics and explains how to use these basic techniques to estimate and model random variation in the context of engineering analysis and design in all types of environments.The first eight chapters cover probability and probability distributions, graphical displays of data and descriptive statistics, combinations of random variables and propagation of error, statistical inference, bivariate distributions and correlation, linear regression on a single predictor variable, and the measurement error model. This leads to chapters including multiple regression; comparisons of several means and split-plot designs together with analysis of variance; probability models; and sampling strategies.Key features: All examples based on work in industry, consulting to industry, and research for industry Examples and case studies include all engineering disciplinesEmphasis on probabilistic modeling including decision trees, Markov chains and processes, and structure functionsIntuitive explanations are followed by succinct mathematical justificationsEmphasis on random number generation that is used for stochastic simulations of engineering systems, demonstration of key concepts, and implementation of bootstrap methods for inferenceUse of MATLAB and the open source software R, both of which have an extensive range of statistical functions for standard analyses and also enable programing of specific applicationsUse of multiple regression for times series models and analysis of factorial and central composite designs Inclusion of topics such as Weibull analysis of failure times and split-plot designs that are commonly used in industry but are not usually included in introductory textbooksExperiments designed to show fundamental concepts that have been tested with large classes working in small groupsWebsite with additional materials that is regularly updated

"The level is appropriate for an upper-level undergraduate or graduate-level statistics major. Sampling: Design and Analysis (SDA) will also benefit a non-statistics major with a desire to understand the concepts of sampling from a finite population. A student with patience to delve into the rigor of survey statistics will gain even more from the content that SDA offers. The updates to SDA have potential to enrich traditional survey sampling classes at both the undergraduate and graduate levels. The new discussions of low response rates, non-probability surveys, and internet as a data collection mode hold particular value, as these statistical issues have become increasingly important in survey practice in recent years… I would eagerly adopt the new edition of SDA as the required textbook." (Emily Berg, Iowa State University)What is the unemployment rate? What is the total area of land planted with soybeans? How many persons have antibodies to the virus causing COVID-19? Sampling: Design and Analysis, Third Edition shows you how to design and analyze surveys to answer these and other questions. This authoritative text, used as a standard reference by numerous survey organizations, teaches the principles of sampling with examples from social sciences, public opinion research, public health, business, agriculture, and ecology. Readers should be familiar with concepts from an introductory statistics class including probability and linear regression; optional sections contain statistical theory for readers familiar with mathematical statistics.Key Features:Has been thoroughly revised to incorporate recent research and applications.Includes a new chapter on nonprobability samples, and more than 200 new examples and exercises have been added.Teaches the principles of sampling with examples from social sciences, public opinion research, public health, business, agriculture, and ecology.SDA’s companion website contains data sets, computer code, and links to two free downloadable supplementary books (also available in paperback) that provide step-by-step guides—with code, annotated output, and helpful tips—for working through the SDA examples. Instructors can use either R or SAS® software.SAS® Software Companion for Sampling: Design and Analysis, Third Edition by Sharon L. Lohr (2022, CRC Press)R Companion for Sampling: Design and Analysis, Third Edition by Yan Lu and Sharon L. Lohr (2022, CRC Press)

Generalized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture – linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory.Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, this book covers all of the above as members of a unified GLMM family of linear models. In addition to essential theory and methodology, this book features a rich collection of examples using SAS® software to illustrate GLMM practice. This second edition is updated to reflect lessons learned and experience gained regarding best practices and modeling choices faced by GLMM practitioners. New to this edition are two chapters focusing on Bayesian methods for GLMMs.Key Features:Most statistical modeling books cover classical linear models or advanced generalized and mixed models; this book covers all members of the GLMM family – classical and advanced modelsIncorporates lessons learned from experience and on-going research to provide up-to-date examples of best practicesIllustrates connections between statistical design and modeling: guidelines for translating study design into appropriate model and in-depth illustrations of how to implement these guidelines; use of GLMM methods to improve planning and designDiscusses the difference between marginal and conditional models, differences in the inference space they are intended to address and when each type of model is appropriateIn addition to likelihood-based frequentist estimation and inference, provides a brief introduction to Bayesian methods for GLMMs

This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation.FeaturesThe classic graduate-level textbook on statistical inferenceDevelops elements of statistical theory from first principles of probabilityWritten in a lucid style accessible to anyone with some background in calculusCovers all key topics of a standard course in inferenceHundreds of examples throughout to aid understandingEach chapter includes an extensive set of graduated exercisesStatistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations.This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

Multi-state models provide a statistical framework for studying longitudinal data on subjects when focus is on the occurrence of events that the subjects may experience over time. They find application particularly in biostatistics, medicine, and public health. The book includes mathematical detail which can be skipped by readers more interested in the practical examples. It is aimed at biostatisticians and at readers with an interest in the topic having a more applied background, such as epidemiology. This book builds on several courses the authors have taught on the subject.Key Features:Intensity-based and marginal models.Survival data, competing risks, illness-death models, recurrent events.Includes a full chapter on pseudo-values.Intuitive introductions and mathematical details.Practical examples of event history data.Exercises.Software code in R and SAS and the data used in the book, as well as solutions to the exercises, can be found on the book’s webpage: https://multi-state-book.github.io/companion.

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix.Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers.Features* Presents the mathematical foundations of spatial statistics.* Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology.* Gives pointers to the literature to facilitate further study.* Provides example code in R to encourage the student to experiment.* Offers exercises and their solutions to test and deepen understanding.The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix.Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers.Features* Presents the mathematical foundations of spatial statistics.* Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology.* Gives pointers to the literature to facilitate further study.* Provides example code in R to encourage the student to experiment.* Offers exercises and their solutions to test and deepen understanding.The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

From a review of the first edition: "Modern Data Science with R… is rich with examples and is guided by a strong narrative voice. What’s more, it presents an organizing framework that makes a convincing argument that data science is a course distinct from applied statistics" (The American Statistician).Modern Data Science with R is a comprehensive data science textbook for undergraduates that incorporates statistical and computational thinking to solve real-world data problems. Rather than focus exclusively on case studies or programming syntax, this book illustrates how statistical programming in the state-of-the-art R/RStudio computing environment can be leveraged to extract meaningful information from a variety of data in the service of addressing compelling questions.The second edition is updated to reflect the growing influence of the tidyverse set of packages. All code in the book has been revised and styled to be more readable and easier to understand. New functionality from packages like sf, purrr, tidymodels, and tidytext is now integrated into the text. All chapters have been revised, and several have been split, re-organized, or re-imagined to meet the shifting landscape of best practice.

An Introduction to Nonparametric Statistics presents techniques for statistical analysis in the absence of strong assumptions about the distributions generating the data. Rank-based and resampling techniques are heavily represented, but robust techniques are considered as well. These techniques include one-sample testing and estimation, multi-sample testing and estimation, and regression.Attention is paid to the intellectual development of the field, with a thorough review of bibliographical references. Computational tools, in R and SAS, are developed and illustrated via examples. Exercises designed to reinforce examples are included.Features Rank-based techniques including sign, Kruskal-Wallis, Friedman, Mann-Whitney and Wilcoxon tests are presented Tests are inverted to produce estimates and confidence intervals Multivariate tests are explored Techniques reflecting the dependence of a response variable on explanatory variables are presented Density estimation is explored The bootstrap and jackknife are discussedThis text is intended for a graduate student in applied statistics. The course is best taken after an introductory course in statistical methodology, elementary probability, and regression. Mathematical prerequisites include calculus through multivariate differentiation and integration, and, ideally, a course in matrix algebra.

The goals of this text are to develop the skills and an appreciation for the richness and versatility of modern time series analysis as a tool for analyzing dependent data. A useful feature of the presentation is the inclusion of nontrivial data sets illustrating the richness of potential applications to problems in the biological, physical, and social sciences as well as medicine. The text presents a balanced and comprehensive treatment of both time and frequency domain methods with an emphasis on data analysis.Numerous examples using data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and the analysis of economic and financial problems. The text can be used for a one semester/quarter introductory time series course where the prerequisites are an understanding of linear regression, basic calculus-based probability skills, and math skills at the high school level. All of the numerical examples use the R statistical package without assuming that the reader has previously used the software.

An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. the book assumes that readers are familiar with the content covered in a typical undergraduate-level introductory statistics course. Readers will also, ideally, have some experience with undergraduate-level probability, calculus, and the R statistical software. Readers without this background will still be able to follow along so long as theyare eager to pick up these tools on the fly as all R code is provided.Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum.Features• Utilizes data-driven examples and exercises.• Emphasizes the iterative model building and evaluation process.• Surveys an interconnected range of multivariable regression and classification models.• Presents fundamental Markov chain Monte Carlo simulation.• Integrates R code, including RStan modeling tools and the bayesrules package.• Encourages readers to tap into their intuition and learn by doing.• Provides a friendly and inclusive introduction to technical Bayesian concepts.• Supports Bayesian applications with foundational Bayesian theory.

This book provides the tools, the methods, and the theory to meet the challenges of contemporary data science applied to geographic problems and data. In the new world of pervasive, large, frequent, and rapid data, there are new opportunities to understand and analyze the role of geography in everyday life. Geographic Data Science with Python introduces a new way of thinking about analysis, by using geographical and computational reasoning, it shows the reader how to unlock new insights hidden within data.Key Features:Showcases the excellent data science environment in PythonProvides examples for readers to replicate, adapt, extend, and improveCovers the crucial knowledge needed by geographic data scientistsIt presents concepts in a far more geographic way than competing textbooks, covering spatial data, mapping, and spatial statistics whilst covering concepts, such as clusters and outliers, as geographic concepts.Intended for data scientists, GIScientists, and geographers, the material provided in this book is of interest due to the manner in which it presents geospatial data, methods, tools, and practices in this new field.

Survival analysis is crucial in many fields, including biomedical research, actuarial science, reliability analysis, business and customer analytics, econometrics, and social science. It has witnessed significant advancements in recent decades. However, most of this progress remains in scattered theoretical and applied publications, often focusing on exploratory analysis rather than the design and analysis of clinical trials. Non-proportional hazards are less well addressed. Competing risks are frequently overlooked, and the counting process approach often remains a mystery to many practitioners. Consequently, these critical topics are often not well understood or thoroughly analyzed.Survival Analysis: Principles and Applications in Clinical Trials and Beyond aims to address these gaps. It provides an up-to-date and reader-friendly account of topics, progressing from the log-rank test, stratified analysis, and Cox regression to more advanced analyses. Heuristic arguments are used, leaving rigorous results to the appendices. The book dedicates separate chapters to topics such as clinical trials basics, modeling and analysis for non-proportional hazards, testing and summarizing treatment effects, trial design and interim monitoring, and the analysis of terminal and non-terminal events. A separate chapter is also devoted to detailed martingale heuristics beyond what is typically offered in other texts. Furthermore, a new contribution to recurrent event analysis is the rigorous formulations of marginal models and an exploration of related properties for statistical applications. The often overlooked one- and two-sample cases are also discussed.This book provides an exposition of both the theory and practical applications of survival analysis, covering traditional topics and more recent advancements. It illustrates the methods with real world data, discussing the strengths and limitations of various approaches, and emphasizing modeling assumptions and interpretations. The three appendices offer overviews of modern analytic frameworks pivotal for understanding and developing challenging yet vital statistical solutions. R packages are also available for newer methods. It is an up-to-date, critical and accessible textbook for graduate students and researchers across industry, government, or academia that will enhance their understanding of complex topics, boosting their confidence in exploring different methods and interpreting the findings. It also encourages a critical evaluation of current literature and motivates the readers to develop new research ideas.Key Features:Emphasis on model interpretations and comparison of different methodsIntuitive explanations and heuristic derivation of the methodsReal large trial data applications and R packages for newer methodologiesInclusion of more recently researched topicsModern analytical methods applied to rigorous asymptotics for key problems (in appendices)

Nonparametric statistical methods minimize the number of assumptions that need to be made about the distribution of data being analysed, unlike classical parametric methods. As such, they are an essential part of a statistician’s armoury, and this book is an essential resource in their application. Starting from the basics of statistics, it takes the reader through the main nonparametric approaches with an emphasis on carefully explained examples backed up by use of the R programming language.Key features of this fully revised and extended fifth edition include the following:An introductory chapter that provides a gentle introduction to the basics of statistics, including types of data, hypothesis testing, confidence intervals and ethical issuesAn R package containing functions that have been written for the examples in the text and the exercisesSummary bullet points at the end of each section to enable the reader to locate important principles quicklyA case study from medical research to demonstrate nonparametric approaches to the data analysisExamples fully integrated into the text, drawn from published research on contemporary issues, with more detail given in their explanationExtensive exercises along with complete solutions that allow the reader to test their understanding of the materialArticles used in the examples and exercises carefully chosen to enable readers to identify up-to-date literature in their field for research, publications and teaching materialNumerous historical references throughout the text, from which to explore the origins of nonparametric methodsApplied Nonparametric Statistical Methods, Fifth Edition, is a comprehensive course text in nonparametric techniques suitable for undergraduate students of mathematics and statistics. It assumes only basic previous experience of statistics, and with algebra kept to a minimum, it is also ideal for quantitative methods modules delivered to undergraduate or postgraduate students in science, business and health service training. It is an invaluable resource for researchers, medical practitioners, business managers, research and development staff, and others needing to interpret quantitative information. Suitable for self-directed learning in continuing professional development, it also acts as a handy accessible reference manual.

Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. Like its bestselling predecessors, the fourth edition of Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates a large number of statistical methods with an emphasis on biological applications. The focus is now on the use of randomization, bootstrapping, and Monte Carlo methods in constructing confidence intervals and doing tests of significance. The text provides comprehensive coverage of computer-intensive applications, with data sets available online.Features Presents an overview of computer-intensive statistical methods and applications in biology Covers a wide range of methods including bootstrap, Monte Carlo, ANOVA, regression, and Bayesian methods Makes it easy for biologists, researchers, and students to understand the methods used Provides information about computer programs and packages to implement calculations, particularly using R code Includes a large number of real examples from a range of biological disciplinesWritten in an accessible style, with minimal coverage of theoretical details, this book provides an excellent introduction to computer-intensive statistical methods for biological researchers. It can be used as a course text for graduate students, as well as a reference for researchers from a range of disciplines. The detailed, worked examples of real applications will enable practitioners to apply the methods to their own biological data.

Bayesian Networks: With Examples in R, Second Edition introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples illustrate each step of the modelling process and discuss side by side the underlying theory and its application using R code. The examples start from the simplest notions and gradually increase in complexity. In particular, this new edition contains significant new material on topics from modern machine-learning practice: dynamic networks, networks with heterogeneous variables, and model validation.The first three chapters explain the whole process of Bayesian network modelling, from structure learning to parameter learning to inference. These chapters cover discrete, Gaussian, and conditional Gaussian Bayesian networks. The following two chapters delve into dynamic networks (to model temporal data) and into networks including arbitrary random variables (using Stan). The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R packages and other software implementing Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein-signalling network published in Science and a probabilistic graphical model for predicting the composition of different body parts.Covering theoretical and practical aspects of Bayesian networks, this book provides you with an introductory overview of the field. It gives you a clear, practical understanding of the key points behind this modelling approach and, at the same time, it makes you familiar with the most relevant packages used to implement real-world analyses in R. The examples covered in the book span several application fields, data-driven models and expert systems, probabilistic and causal perspectives, thus giving you a starting point to work in a variety of scenarios.Online supplementary materials include the data sets and the code used in the book, which will all be made available from https://www.bnlearn.com/book-crc-2ed/

Surrogates: a graduate textbook, or professional handbook, on topics at the interface between machine learning, spatial statistics, computer simulation, meta-modeling (i.e., emulation), design of experiments, and optimization. Experimentation through simulation, "human out-of-the-loop" statistical support (focusing on the science), management of dynamic processes, online and real-time analysis, automation, and practical application are at the forefront. Topics include: Gaussian process (GP) regression for flexible nonparametric and nonlinear modeling. Applications to uncertainty quantification, sensitivity analysis, calibration of computer models to field data, sequential design/active learning and (blackbox/Bayesian) optimization under uncertainty. Advanced topics include treed partitioning, local GP approximation, modeling of simulation experiments (e.g., agent-based models) with coupled nonlinear mean and variance (heteroskedastic) models. Treatment appreciates historical response surface methodology (RSM) and canonical examples, but emphasizes contemporary methods and implementation in R at modern scale. Rmarkdown facilitates a fully reproducible tour, complete with motivation from, application to, and illustration with, compelling real-data examples.Presentation targets numerically competent practitioners in engineering, physical, and biological sciences. Writing is statistical in form, but the subjects are not about statistics. Rather, they’re about prediction and synthesis under uncertainty; about visualization and information, design and decision making, computing and clean code.

This book is a fresh approach to a calculus based, first course in probability and statistics, using R throughout to give a central role to data and simulation.The book introduces probability with Monte Carlo simulation as an essential tool. Simulation makes challenging probability questions quickly accessible and easily understandable. Mathematical approaches are included, using calculus when appropriate, but are always connected to experimental computations. Using R and simulation gives a nuanced understanding of statistical inference. The impact of departure from assumptions in statistical tests is emphasized, quantified using simulations, and demonstrated with real data. The book compares parametric and non-parametric methods through simulation, allowing for a thorough investigation of testing error and power. The text builds R skills from the outset, allowing modern methods of resampling and cross validation to be introduced along with traditional statistical techniques.Fifty-two data sets are included in the complementary R package fosdata. Most of these data sets are from recently published papers, so that you are working with current, real data, which is often large and messy. Two central chapters use powerful tidyverse tools (dplyr, ggplot2, tidyr, stringr) to wrangle data and produce meaningful visualizations. Preliminary versions of the book have been used for five semesters at Saint Louis University, and the majority of the more than 400 exercises have been classroom tested.The exercises in the book have been added to to the free and open online homework system myopenmath (https://www.myopenmath.com/) which may be useful to instructors.

This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering.The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth.This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.

Many scientists and technologists would like to carry out their own statistical analyses without reference to a professional statistician. Often, however, they have no knowledge of statistics or otherwise do not know how to apply it to research and development problems. The first edition of Statistics in Research and Development was written for these people. The second edition brings the book up-to-date.The text is divided into two parts; the first introduces basic but very important statistical techniques whilst the second part presents the modern powerful methods of data analysis that are particularly useful in modern research and development. Problems are provided at the end of each chapter with worked solutions provided at the end of the book. A problem-centered approach is used throughout and care has been taken to choose problems with which the scientist or technologist can identify. The results of the statistical analyses are reinterpreted into the language of the scientist. Mathematics is kept to a minimum and the assumptions underlying each technique are clearly explained. All the techniques introduced are powerful and proven, and commercial computer programs are available for many of them.

GENSTAT is a general purpose statistical computing system with a flexible command language operating on a variety of data structures. It may be used on a number of computer ranges, either interactively for exploratory data analysis, or in batch mode for standard data analysis.The great flexibility of GENSTAT is demonstrated in this handbook by analysing the wide range of examples discussed in Applied Statistics - Principles and Examples (Cox and Snell, 1981). GENSTAT programs are listed for each of the examples. Most of the data sets are small but often it is these seemingly small problems which involve the most tricky statistical and computational procedures. This handbook is self-contained although for a full description of the analysis and interpretation it should be used in parallel with Applied Statistics - Principles and Examples.

Introduction to Design and Analysis of Scientific Studies exposes undergraduate and graduate students to the foundations of classical experimental design and observational studies through a modern framework - The Rubin Causal Model. A causal inference framework is important in design, data collection and analysis since it provides a framework for investigators to readily evaluate study limitations and draw appropriate conclusions. R is used to implement designs and analyse the data collected.Features:Classical experimental design with an emphasis on computation using tidyverse packages in R.Applications of experimental design to clinical trials, A/B testing, and other modern examples.Discussion of the link between classical experimental design and causal inference.The role of randomization in experimental design and sampling in the big data era.Exercises with solutions.Instructor slides in RMarkdown, a new R package will be developed to be used with book, and a bookdown version of the book will be freely available. The proposed book will emphasize ethics, communication and decision making as part of design, data analysis, and statistical thinking.

Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.

Design of experiments is, in essence, a disciplined way to learn about cause and effect. Modern experiments can involve a few to millions of units and hundreds or thousands of covariates. These settings demand tools that are flexible, transparent, and faithful to the underlying design in order reach reliable conclusions about which interventions work and which ones do not. This book provides a modern, accessible, and computationally supported introduction to experimental design grounded firmly in randomization and the formulation of ideas and methods in terms of potential outcomes. Instead of prescribing a model for each design, we begin with the treatment assignment mechanism and link it directly to the observed outcomes through the potential outcomes framework. This formulation illuminates how changing the design changes the analysis, and it naturally distinguishes finite-population inference from super-population modeling. The book also incorporates new developments at the interface of causal inference and experimental design, many stemming from the authors’ recent collaborative research efforts.Key Features:Strengthens the link between design and analysis, enabling students to see immediately how the structure of an experiment shapes the exact tools used to analyze it.Teaches foundational concepts without assuming linear-model assumptions.Equips readers with the tools needed to analyze non-standard and complex experiments, whose randomization mechanisms fall outside the scope of traditional textbooks.Support students with limited programming experience by providing algorithms and code throughout the book, enabling them to implement randomization-based methods easily and efficiently.This book is a textbook for one/two semester course on introductory experimental design.

Theory of Statistical Inference is designed as a reference on statistical inference for researchers and students at the graduate or advanced undergraduate level. It presents a unified treatment of the foundational ideas of modern statistical inference, and would be suitable for a core course in a graduate program in statistics or biostatistics. The emphasis is on the application of mathematical theory to the problem of inference, leading to an optimization theory allowing the choice of those statistical methods yielding the most efficient use of data. The book shows how a small number of key concepts, such as sufficiency, invariance, stochastic ordering, decision theory and vector space algebra play a recurring and unifying role. The volume can be divided into four sections. Part I provides a review of the required distribution theory. Part II introduces the problem of statistical inference. This includes the definitions of the exponential family, invariant and Bayesian models. Basic concepts of estimation, confidence intervals and hypothesis testing are introduced here. Part III constitutes the core of the volume, presenting a formal theory of statistical inference. Beginning with decision theory, this section then covers uniformly minimum variance unbiased (UMVU) estimation, minimum risk equivariant (MRE) estimation and the Neyman-Pearson test. Finally, Part IV introduces large sample theory. This section begins with stochastic limit theorems, the δ-method, the Bahadur representation theorem for sample quantiles, large sample U-estimation, the Cramér-Rao lower bound and asymptotic efficiency. A separate chapter is then devoted to estimating equation methods. The volume ends with a detailed development of large sample hypothesis testing, based on the likelihood ratio test (LRT), Rao score test and the Wald test. Features This volume includes treatment of linear and nonlinear regression models, ANOVA models, generalized linear models (GLM) and generalized estimating equations (GEE). An introduction to decision theory (including risk, admissibility, classification, Bayes and minimax decision rules) is presented. The importance of this sometimes overlooked topic to statistical methodology is emphasized. The volume emphasizes throughout the important role that can be played by group theory and invariance in statistical inference. Nonparametric (rank-based) methods are derived by the same principles used for parametric models and are therefore presented as solutions to well-defined mathematical problems, rather than as robust heuristic alternatives to parametric methods. Each chapter ends with a set of theoretical and applied exercises integrated with the main text. Problems involving R programming are included. Appendices summarize the necessary background in analysis, matrix algebra and group theory.

Modern computer-intensive statistical methods play a key role in solving many problems across a wide range of scientific disciplines. Like its bestselling predecessors, the fourth edition of Randomization, Bootstrap and Monte Carlo Methods in Biology illustrates a large number of statistical methods with an emphasis on biological applications. The focus is now on the use of randomization, bootstrapping, and Monte Carlo methods in constructing confidence intervals and doing tests of significance. The text provides comprehensive coverage of computer-intensive applications, with data sets available online.Features Presents an overview of computer-intensive statistical methods and applications in biology Covers a wide range of methods including bootstrap, Monte Carlo, ANOVA, regression, and Bayesian methods Makes it easy for biologists, researchers, and students to understand the methods used Provides information about computer programs and packages to implement calculations, particularly using R code Includes a large number of real examples from a range of biological disciplinesWritten in an accessible style, with minimal coverage of theoretical details, this book provides an excellent introduction to computer-intensive statistical methods for biological researchers. It can be used as a course text for graduate students, as well as a reference for researchers from a range of disciplines. The detailed, worked examples of real applications will enable practitioners to apply the methods to their own biological data.

A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects.Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects takes a first step in developing a full theory of richly parameterized models, which would allow statisticians to better understand their analysis results. The author examines what is known and unknown about mixed linear models and identifies research opportunities.The first two parts of the book cover an existing syntax for unifying models with random effects. The text explains how richly parameterized models can be expressed as mixed linear models and analyzed using conventional and Bayesian methods.In the last two parts, the author discusses oddities that can arise when analyzing data using these models. He presents ways to detect problems and, when possible, shows how to mitigate or avoid them. The book adapts ideas from linear model theory and then goes beyond that theory by examining the information in the data about the mixed linear model’s covariance matrices.Each chapter ends with two sets of exercises. Conventional problems encourage readers to practice with the algebraic methods and open questions motivate readers to research further. Supporting materials, including datasets for most of the examples analyzed, are available on the author’s website.