The present monograph is primarily an outgrowth of our own re search on certain aspects of Bayesian inference in finite population sampling. Finite population sampling has been an integral part of statistics since its beginning. The topic continues its impact in the theory and practice of statistics, especially for researchers in survey sampling. Inference for finite population sampling utilizes prior information either explicitly or implicitly. Bayesian inference makes explicit use of this information as part of the model. This is in striking con trast to design- based inference in survey sampling where prior knowledge is incorporated only as auxiliary information. On the other hand there is a elose relationship between the Bayesian ap proach and the superpopulation approach, although they differ in their foundational interpretations. Operationally, however, the dif ference is much less pronounced as many estimators obtained via superpopulation models are also obtainable as Bayes estimators, and vice versa. This monograph, does not aim to provide a complete up-to-date account of the Bayesian literature in finite population sampling. Rather, it treats the topics reflecting the authors' personal inter ests. Its main aim is to demonstrate that a variety of levels of prior information can be used in survey sampling in a Bayesian man ner. Situations considered range from a noninformative Bayesian justification of standard frequentist methods when the only prior information available is the belief in the exchangeablility of the units to a full-fledged Bayesian model."

With the aim to better understand nature, mathematical tools are being used nowadays in many different fields. The concept of integral transforms, in particular, has been found to be a useful mathematical tool for solving a variety of problems not only in mathematics, but also in various other branches of science, engineering, and technology. Integral Transforms and Engineering: Theory, Methods, and Applications presents a mathematical analysis of integral transforms and their applications. The book illustrates the possibility of obtaining transfer functions using different integral transforms, especially when mapping any function into the frequency domain. Various differential operators, models, and applications are included such as classical derivative, Caputo derivative, Caputo-Fabrizio derivative, and Atangana-Baleanu derivative. This book is a useful reference for practitioners, engineers, researchers, and graduate students in mathematics, applied sciences, engineering, and technology fields.

This work provides descriptions, explanations and examples of the Bayesian approach to statistics, demonstrating the utility of Bayesian methods for analyzing real-world problems in the health sciences. The work considers the individual components of Bayesian analysis.;College or university bookstores may order five or more copies at a special student price, available on request from Marcel Dekker, Inc.

The analysis, prediction and interpolation of economic and other time series has a long history and many applications. Major new developments are taking place, driven partly by the need to analyze financial data. The five papers in this book describe those new developments from various viewpoints and are intended to be an introduction accessible to readers from a range of backgrounds. The book arises out of the second Seminaire European de Statistique (SEMSTAT) held in Oxford in December 1994. This brought together young statisticians from across Europe, and a series of introductory lectures were given on topics at the forefront of current research activity. The lectures form the basis for the five papers contained in the book. The papers by Shephard and Johansen deal respectively with time series models for volatility, i.e. variance heterogeneity, and with cointegration. Clements and Hendry analyze the nature of prediction errors. A complementary review paper by Laird gives a biometrical view of the analysis of short time series. Finally Astrup and Nielsen give a mathematical introduction to the study of option pricing. Whilst the book draws its primary motivation from financial series and from multivariate econometric modelling, the applications are potentially much broader.

By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.

Many technological, socio-economic, environmental, biomedical phenomena exhibit an underlying graph structure. Valued graph allows one to incorporate the connections or links among the population units in addition. The links may provide effectively access to the part of population that is the primary target, which is the case for many unconventional sampling methods, such as indirect, network, line-intercept or adaptive cluster sampling. Or, one may be interested in the structure of the connections, in terms of the corresponding graph properties or parameters, such as when various breadth- or depth-first non-exhaustive search algorithms are applied to obtain compressed views of large often dynamic graphs. Graph sampling provides a statistical approach to study real graphs from either of these perspectives. It is based on exploring the variation over all possible sample graphs (or subgraphs) which can be taken from the given population graph, by means of the relevant known sampling probabilities. The resulting design-based inference is valid whatever the unknown properties of the given real graphs. One-of-a-kind treatise of multidisciplinary topics relevant to statistics, mathematics and data science. Probabilistic treatment of breadth-first and depth-first non-exhaustive search algorithms in graphs. Presenting cutting-edge theory and methods based on latest research. Pathfinding for future research on sampling from real graphs. Graph Sampling can primarily be used as a resource for researchers working with sampling or graph problems, and as the basis of an advanced course for post-graduate students in statistics, mathematics and data science.

Learn the basics of white noise theory with White Noise Distribution Theory. This book covers the mathematical foundation and key applications of white noise theory without requiring advanced knowledge in this area. This instructive text specifically focuses on relevant application topics such as integral kernel operators, Fourier transforms, Laplacian operators, white noise integration, Feynman integrals, and positive generalized functions. Extremely well-written by one of the field's leading researchers, White Noise Distribution Theory is destined to become the definitive introductory resource on this challenging topic.

This text describes regression-based approaches to analyzing longitudinal and repeated measures data. It emphasizes statistical models, discusses the relationships between different approaches, and uses real data to illustrate practical applications. It uses commercially available software when it exists and illustrates the program code and output. The data appendix provides many real data sets-beyond those used for the examples-which can serve as the basis for exercises.

Multiple Comparisons covers all-pairwise comparisons, multiple comparisons with the best, and multiple comparisons with a control. Confidence intervals methods and stepwise methods are described. Abuses and misconceptions are exposed, and the reader is guided to the correct method for each problem. Connections with bioequivalence, drug stability, and toxicity studies are discussed. Applications are illustrated with real data, analyzed by computer packages. Extension to the General Linear Model is provided.

Introduce the steps from association to causation that follow after adjustments are complete. Gives good analysis of weighting and matching in model-based adjustments. Useful for thos who examine evidence of the effects on human beings of treatments, policies or exposures.

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.

In a family study of breast cancer, epidemiologists in Southern California increase the power for detecting a gene-environment interaction. In Gambia, a study helps a vaccination program reduce the incidence of Hepatitis B carriage. Archaeologists in Austria place a Bronze Age site in its true temporal location on the calendar scale. And in France, researchers map a rare disease with relatively little variation.
Each of these studies applied Markov chain Monte Carlo methods to produce more accurate and inclusive results. General state-space Markov chain theory has seen several developments that have made it both more accessible and more powerful to the general statistician. Markov Chain Monte Carlo in Practice introduces MCMC methods and their applications, providing some theoretical background as well. The authors are researchers who have made key contributions in the recent development of MCMC methodology and its application.
Considering the broad audience, the editors emphasize practice rather than theory, keeping the technical content to a minimum. The examples range from the simplest application, Gibbs sampling, to more complex applications. The first chapter contains enough information to allow the reader to start applying MCMC in a basic way. The following chapters cover main issues, important concepts and results, techniques for implementing MCMC, improving its performance, assessing model adequacy, choosing between models, and applications and their domains.
Markov Chain Monte Carlo in Practice is a thorough, clear introduction to the methodology and applications of this simple idea with enormous potential. It shows the importance of MCMC in real applications, such as archaeology, astronomy, biostatistics, genetics, epidemiology, and image analysis, and provides an excellent base for MCMC to be applied to other fields as well.

Learn shocking stats and facts that will surprise you, expand your knowledge, and help you impress your friends! Astonish yourself and your friends with Stats to Blow Your Mind & Everyone Else You're Talking To. Seeing is believing with the many intriguing charts and graphs in this book. Take your learning on the road, this book is perfect for reading during family vacations or to friends at parties. This is the perfect gift for someone who loves to learn. Spark your own curiosity with the compelling statistics in Stats to Blow Your Mind & Everyone Else You're Talking To.

With an emphasis on social science applications, Event History Analysis with R, Second Edition, presents an introduction to survival and event history analysis using real-life examples. Since publication of the first edition, focus in the field has gradually shifted towards the analysis of large and complex datasets. This has led to new ways of tabulating and analysing tabulated data with the same precision and power as that of an analysis of the full data set. Tabulation also makes it possible to share sensitive data with others without violating integrity. The new edition extends on the content of the first by both improving on already given methods and introducing new methods. There are two new chapters, Explanatory Variables and Regression, and Register- Based Survival Data Models. The book has been restructured to improve the flow, and there are significant updates to the computing in the supporting R package. Features * Introduction to survival and event history analysis and how to solve problems with incomplete data using Cox regression. * Parametric proportional hazards models, including the Weibull, Exponential, Extreme Value, and Gompertz distributions. * Parametric accelerated failure time models with the Lognormal, Loglogistic, Gompertz, Exponential, Extreme Value, and Weibull distributions. * Proportional hazards models for occurrence/exposure data, useful with tabular and register based data, often with a huge amount of observed events. * Special treatments of external communal covariates, selections from the Lexis diagram, and creating period as well as cohort statistics. * "Weird bootstrap" sampling suitable for Cox regression with small to medium-sized data sets. * Supported by an R package (https://CRAN.R-project.org/package=eha), including code and data for most examples in the book. * A dedicated home page for the book at http://ehar.se/r/ehar2 This substantial update to this popular book remains an excellent resource for researchers and practitioners of applied event history analysis and survival analysis. It can be used as a text for a course for graduate students or for self-study.

"Offers a comprehensive, unified presentation of statistical designs and methods of analysis for all stages of pharmaceutical development--emphasizing biopharmaceutical applications and demonstrating statistical techniques with real-world examples."

Second Edition offers a comprehensive presentation of scientific sampling principles and shows how to design a sample survey and analyze the resulting data. Demonstrates the validity of theorems and statements without resorting to detailed proofs.

This text includes coverage of asymptotic expansions taking into account the cases when the number of summands comparable with the sum is less than or equal to two and asymptotic expansions of the probabilities of large deviations and non-uniform estimates of remainders in CLT.

Statistical Analysis of Contingency Tables is an invaluable tool for statistical inference in contingency tables. It covers effect size estimation, confidence intervals, and hypothesis tests for the binomial and the multinomial distributions, unpaired and paired 2x2 tables, rxc tables, ordered rx2 and 2xc tables, paired cxc tables, and stratified tables. For each type of table, key concepts are introduced, and a wide range of intervals and tests, including recent and unpublished methods and developments, are presented and evaluated. Topics such as diagnostic accuracy, inter-rater reliability, and missing data are also covered. The presentation is concise and easily accessible for readers with diverse professional backgrounds, with the mathematical details kept to a minimum. For more information, including a sample chapter and software, please visit the authors' website.

Nonlinear measurement data arise in a wide variety of biological and biomedical applications, such as longitudinal clinical trials, studies of drug kinetics and growth, and the analysis of assay and laboratory data. Nonlinear Models for Repeated Measurement Data provides the first unified development of methods and models for data of this type, with a detailed treatment of inference for the nonlinear mixed effects and its extensions. A particular strength of the book is the inclusion of several detailed case studies from the areas of population pharmacokinetics and pharmacodynamics, immunoassay and bioassay development and the analysis of growth curves.

Confidence Intervals for Discrete Data in Clinical Research is designed as a toolbox for biomedical researchers. Analysis of discrete data is one of the most used yet vexing areas in clinical research. The array of methodologies available in the literature to address the inferential questions for binomial and multinomial data can be a double-edged sword. On the one hand, these methods open a rich avenue of exploration of data; on the other, the wide-ranging and competing methodologies potentially lead to conflicting inferences, adding to researchers' confusion and frustration and also leading to reporting bias. This book addresses the problems that many practitioners experience in choosing and implementing fit for purpose data analysis methods to answer critical inferential questions for binomial and count data. The book is an outgrowth of the authors' collective experience in biomedical research and provides an excellent overview of inferential questions of interest for binomial proportions and rates based on count data, and reviews various solutions to these problems available in the literature. Each chapter discusses the strengths and weaknesses of the methods and suggests practical recommendations. The book's primary focus is on applications in clinical research, and the goal is to provide direct benefit to the users involved in the biomedical field.

The concepts of estimands, analyses (estimators), and sensitivity are interrelated. Therefore, great need exists for an integrated approach to these topics. This book acts as a practical guide to developing and implementing statistical analysis plans by explaining fundamental concepts using accessible language, providing technical details, real-world examples, and SAS and R code to implement analyses. The updated ICH guideline raises new analytic and cross-functional challenges for statisticians. Gaps between different communities have come to surface, such as between causal inference and clinical trialists, as well as among clinicians, statisticians, and regulators when it comes to communicating decision-making objectives, assumptions, and interpretations of evidence. This book lays out a path toward bridging some of these gaps. It offers A common language and unifying framework along with the technical details and practical guidance to help statisticians meet the challenges A thorough treatment of intercurrent events (ICEs), i.e., postrandomization events that confound interpretation of outcomes and five strategies for ICEs in ICH E9 (R1) Details on how estimands, integrated into a principled study development process, lay a foundation for coherent specification of trial design, conduct, and analysis needed to overcome the issues caused by ICEs: A perspective on the role of the intention-to-treat principle Examples and case studies from various areas Example code in SAS and R A connection with causal inference Implications and methods for analysis of longitudinal trials with missing data Together, the authors have offered the readers their ample expertise in clinical trial design and analysis, from an industrial and academic perspective.

First-hand technical expertise – torch has been developed in/by the author’s team at RStudio. Presupposes only a minimal background in mathematics. Presupposes no background in optimization and/or deep learning (but some general ideas about machine learning). Entertaining and fun to read (at least that’s the intention!). Concept-first approach

Self-contained chapters on the most important applications and methodologies in finance, which can easily be used for the reader’s research or as a reference for courses on empirical finance. Each chapter is reproducible in the sense that the reader can replicate every single figure, table, or number by simply copy-pasting the code we provide. A full-fledged introduction to machine learning with tidymodels based on tidy principles to show how factor selection and option pricing can benefit from Machine Learning methods. Chapter 2 on accessing & managing financial data shows how to retrieve and prepare the most important datasets in the field of financial economics: CRSP and Compustat. The chapter also contains detailed explanations of the most important data characteristics. Each chapter provides exercises that are based on established lectures and exercise classes and which are designed to help students to dig deeper. The exercises can be used for self-studying or as source of inspiration for teaching exercises.

Likelihood and its many associated concepts are of central importance in statistical theory and applications. The theory of likelihood and of likelihood-like objects (pseudo-likelihoods) has undergone extensive and important developments over the past 10 to 15 years, in particular as regards higher order asymptotics. This book provides an account of this field, which is still vigorously expanding. Conditioning and ancillarity underlie the p*-formula, a key formula for the conditional density of the maximum likelihood estimator, given an ancillary statistic. Various types of pseudo-likelihood are discussed, including profile and partial likelihoods. Special emphasis is given to modified profile likelihood and modified directed likelihood, and their intimate connection with the p*-formula. Among the other concepts and tools employed are sufficiency, parameter orthogonality, invariance, stochastic expansions and saddlepoint approximations. Brief reviews are given of the most important properties of exponential and transformation models and these types of model are used as test-beds for the general asymptotic theory. A final chapter briefly discusses a number of more general issues, including prediction and randomization theory. The emphasis is on ideas and methods, and detailed mathematical developments are largely omitted. There are numerous notes and exercises, many indicating substantial further results.

Statistical Methods for Long Term Memory Processes covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that previously appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasizes basic principles and practical applications and provides an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows readers to view statistical approaches in a practical context.

Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the first three chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence.