Математика
Различные книги в жанре МатематикаStatistical and Methodological Aspects of Oral Health Research
Statistical and Methodological Aspects of Oral Health Research provides oral health researchers with an overview of the methodological aspects that are important in planning, conducting and analyzing their research projects whilst also providing biostatisticians with an idea of the statistical problems that arise when tackling oral health research questions. This collection presents critical reflections on oral health research and offers advice on practical aspects of setting up research whilst introducing the reader to basic as well as advanced statistical methodology. Features: An introduction to research methodology and an exposition of the state of the art. A variety of examples from oral health research. Contributions from well-known oral health researchers, epidemiologists and biostatisticians, all of whom have rich experience in this area. Recent developments in statistical methodology prompted by a variety of dental applications. Presenting both an introduction to research methodology and an exposition of the latest advances in oral health research, this book will appeal both beginning and experienced oral health researchers as well as biostatisticians and epidemiologists.
Statistical Analysis and Modelling of Spatial Point Patterns
Spatial point processes are mathematical models used to describe and analyse the geometrical structure of patterns formed by objects that are irregularly or randomly distributed in one-, two- or three-dimensional space. Examples include locations of trees in a forest, blood particles on a glass plate, galaxies in the universe, and particle centres in samples of material. Numerous aspects of the nature of a specific spatial point pattern may be described using the appropriate statistical methods. Statistical Analysis and Modelling of Spatial Point Patterns provides a practical guide to the use of these specialised methods. The application-oriented approach helps demonstrate the benefits of this increasingly popular branch of statistics to a broad audience. The book: Provides an introduction to spatial point patterns for researchers across numerous areas of application Adopts an extremely accessible style, allowing the non-statistician complete understanding Describes the process of extracting knowledge from the data, emphasising the marked point process Demonstrates the analysis of complex datasets, using applied examples from areas including biology, forestry, and materials science Features a supplementary website containing example datasets. Statistical Analysis and Modelling of Spatial Point Patterns is ideally suited for researchers in the many areas of application, including environmental statistics, ecology, physics, materials science, geostatistics, and biology. It is also suitable for students of statistics, mathematics, computer science, biology and geoinformatics.
Variations on Split Plot and Split Block Experiment Designs
A complete and up-to-date discussion of optimal split plot and split block designs Variations on Split Plot and Split Block Experiment Designs provides a comprehensive treatment of the design and analysis of two types of trials that are extremely popular in practice and play an integral part in the screening of applied experimental designs–split plot and split block experiments. Illustrated with numerous examples, this book presents a theoretical background and provides two and three error terms, a thorough review of the recent work in the area of split plot and split blocked experiments, and a number of significant results. Written by renowned specialists in the field, this book features: * Discussions of non-standard designs in addition to coverage of split block and split plot designs * Two chapters on combining split plot and split block designs and missing observations, which are unique to this book and to the field of study * SAS? commands spread throughout the book, which allow readers to bypass tedious computation and reveal startling observations * Detailed formulae and thorough remarks at the end of each chapter * Extensive data sets, which are posted on the book's FTP site The design and analysis approach advocated in Variations on Split Plot and Split Block Experiment Designs is essential in creating tailor-made experiments for applied statisticians from industry, medicine, agriculture, chemistry, and other fields of study.
The Theory of Response-Adaptive Randomization in Clinical Trials
Presents a firm mathematical basis for the use of response-adaptive randomization procedures in practice The Theory of Response-Adaptive Randomization in Clinical Trials is the result of the authors' ten-year collaboration as well as their collaborations with other researchers in investigating the important questions regarding response-adaptive randomization in a rigorous mathematical framework. Response-adaptive allocation has a long history in biostatistics literature; however, largely due to the disastrous ECMO trial in the early 1980s, there is a general reluctance to use these procedures. This timely book represents a mathematically rigorous subdiscipline of experimental design involving randomization and answers fundamental questions, including: How does response-adaptive randomization affect power? Can standard inferential tests be applied following response-adaptive randomization? What is the effect of delayed response? Which procedure is most appropriate and how can «most appropriate» be quantified? How can heterogeneity of the patient population be incorporated? Can response-adaptive randomization be performed with more than two treatments or with continuous responses? The answers to these questions communicate a thorough understanding of the asymptotic properties of each procedure discussed, including asymptotic normality, consistency, and asymptotic variance of the induced allocation. Topical coverage includes: The relationship between power and response-adaptive randomization The general result for determining asymptotically best procedures Procedures based on urn models Procedures based on sequential estimation Implications for the practice of clinical trials Useful for graduate students in mathematics, statistics, and biostatistics as well as researchers and industrial and academic biostatisticians, this book offers a rigorous treatment of the subject in order to find the optimal procedure to use in practice.
Numerical Issues in Statistical Computing for the Social Scientist
At last—a social scientist's guide through the pitfalls of modern statistical computing Addressing the current deficiency in the literature on statistical methods as they apply to the social and behavioral sciences, Numerical Issues in Statistical Computing for the Social Scientist seeks to provide readers with a unique practical guidebook to the numerical methods underlying computerized statistical calculations specific to these fields. The authors demonstrate that knowledge of these numerical methods and how they are used in statistical packages is essential for making accurate inferences. With the aid of key contributors from both the social and behavioral sciences, the authors have assembled a rich set of interrelated chapters designed to guide empirical social scientists through the potential minefield of modern statistical computing. Uniquely accessible and abounding in modern-day tools, tricks, and advice, the text successfully bridges the gap between the current level of social science methodology and the more sophisticated technical coverage usually associated with the statistical field. Highlights include: A focus on problems occurring in maximum likelihood estimation Integrated examples of statistical computing (using software packages such as the SAS, Gauss, Splus, R, Stata, LIMDEP, SPSS, WinBUGS, and MATLAB®) A guide to choosing accurate statistical packages Discussions of a multitude of computationally intensive statistical approaches such as ecological inference, Markov chain Monte Carlo, and spatial regression analysis Emphasis on specific numerical problems, statistical procedures, and their applications in the field Replications and re-analysis of published social science research, using innovative numerical methods Key numerical estimation issues along with the means of avoiding common pitfalls A related Web site includes test data for use in demonstrating numerical problems, code for applying the original methods described in the book, and an online bibliography of Web resources for the statistical computation Designed as an independent research tool, a professional reference, or a classroom supplement, the book presents a well-thought-out treatment of a complex and multifaceted field.
Selection Bias and Covariate Imbalances in Randomized Clinical Trials
Selection bias can, and does, occur, even in randomized clinical trials. Steps need to be taken in order to ensure that this does not compromise the integrity of clinical trials; hence “Selection Bias and Covariate Imbalances in Randomized Clinical Trials” offers a comprehensive treatment of the subject and the methodology involved. This book: Provides an overview of the hierarchy of study designs, and justifies the position of randomised trials at the top of this hierarchy. Discusses the strengths and defects of randomisation, and provides real evidence to justify concern regarding its defects. Outlays the damaging consequences that selection bias causes when it does occur. Considers courses of action that can be taken to manage/ contain the problem. Presents methods that can be used to detect selection bias in randomised trials, and methods to correct for selection bias. Concludes by providing a comprehensive plan for managing baseline imbalances and selection bias in randomised trials, and proposing open problems for future research. Illustrated with case studies, this book introduces groundbreaking ideas and research that will be invaluable to researchers and practitioners who design and analyse clinical trials. It will also be of interest to graduate students within the field of biostatistics.
Statistical Framework for Recreational Water Quality Criteria and Monitoring
With increasing rates of pollution to both land and aquatic environments, regulations for the quality of our waters are necessarily becoming more stringent. In the light of recent epidemiological studies new criteria are being established for the safety of our recreational waters. In order for such criteria to be developed an established statistical framework needs to be in place. Statistical Framework for Recreational Water Quality Criteria and Monitoring offers a practical guide to the statistical methods used for assessing health effects and monitoring and modelling water quality Both traditional and novel sampling designs are discussed. Written by a team of international experts in the field, this book sets out to provide an essential structure for the monitoring of water quality. · Proposes a much-needed framework for the monitoring of water quality, and provides practical guidance on the statistical methods involved. · Covers risk characterization, empirical modelling, sensitivity analysis and measures of robustness. · Details sampling methods and quality control approaches. · Presents crucial, real-life results from recent large-scale studies of water quality, central to the development of the area. · Accompanied by a supplementary website hosting data sets and tools for data analysis. The book is primarily aimed at public health officials, staff of regulatory bodies and students and faculty members of environmental and statistical science courses. There is also much to benefit readers from environmental research and risk analysis.
Bayesian Approaches to Clinical Trials and Health-Care Evaluation
READ ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society. Originating from the Medical Research Council’s biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author’s comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synthesis and cost-effectiveness analysis. Covers a broad array of essential topics, building from the basics to more advanced techniques. Illustrated throughout by detailed case studies and worked examples Includes exercises in all chapters Accessible to anyone with a basic knowledge of statistics Authors are at the forefront of research into Bayesian methods in medical research Accompanied by a Web site featuring data sets and worked examples using Excel and WinBUGS – the most widely used Bayesian modelling package Bayesian Approaches to Clinical Trials and Health-Care Evaluation is suitable for students and researchers in medical statistics, statisticians in the pharmaceutical industry, and anyone involved in conducting clinical trials and assessment of health-care technology.
Robust Statistics
A new edition of this popular text on robust statistics, thoroughly updated to include new and improved methods and focus on implementation of methodology using the increasingly popular open-source software R. Classical statistics fail to cope well with outliers associated with deviations from standard distributions. Robust statistical methods take into account these deviations when estimating the parameters of parametric models, thus increasing the reliability of fitted models and associated inference. This new, second edition of Robust Statistics: Theory and Methods (with R) presents a broad coverage of the theory of robust statistics that is integrated with computing methods and applications. Updated to include important new research results of the last decade and focus on the use of the popular software package R, it features in-depth coverage of the key methodology, including regression, multivariate analysis, and time series modeling. The book is illustrated throughout by a range of examples and applications that are supported by a companion website featuring data sets and R code that allow the reader to reproduce the examples given in the book. Unlike other books on the market, Robust Statistics: Theory and Methods (with R) offers the most comprehensive, definitive, and up-to-date treatment of the subject. It features chapters on estimating location and scale; measuring robustness; linear regression with fixed and with random predictors; multivariate analysis; generalized linear models; time series; numerical algorithms; and asymptotic theory of M-estimates. Explains both the use and theoretical justification of robust methods Guides readers in selecting and using the most appropriate robust methods for their problems Features computational algorithms for the core methods Robust statistics research results of the last decade included in this 2nd edition include: fast deterministic robust regression, finite-sample robustness, robust regularized regression, robust location and scatter estimation with missing data, robust estimation with independent outliers in variables, and robust mixed linear models. Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is an ideal resource for researchers, practitioners, and graduate students in statistics, engineering, computer science, and physical and social sciences.
Mathematical Statistics
Presents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function This book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. Mathematical Statistics: An Introduction to Likelihood Based Inference makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematical statistics along with their proofs. In addition to the connected chapters mentioned above, Mathematical Statistics covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. Prepares students with the tools needed to be successful in their future work in statistics data science Includes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage Emphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties Includes sections on Bayesian estimation and credible intervals Features examples, problems, and solutions Mathematical Statistics: An Introduction to Likelihood Based Inference is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and/or statistical inference.