Statistical Models For Proportions And Probabilities

​Methods for making inferences from data about one or more probabilities and proportions are a fundamental part of a statistician’s toolbox and statistics courses. Unfortunately many of the quick, approximate methods currently taught have recently been found to be inappropriate. This monograph gives an up-to-date review of recent research on the topic and presents both exact methods and helpful approximations. Detailed theory is also presented for the different distributions involved, and can be used in a classroom setting. It will be useful for those teaching statistics at university level and for those involved in statistical consulting.

Das für Fachleute und fortgeschrittene Studenten konzipierte Buch beschäftigt sich mit dem Entwurf und der Analyse von Untersuchungen, Studien und Experimenten, bei denen qualitative und kategorische Daten anfallen. - jetzt in dritter Auflage - neue Informationen unter anderem zur logistischen Regression, zur Binomialverteilung, zu Daten von (zufälligen) Stichproben und zu den Delta-Methoden für Multinomialfrequenzen - Buch ist auf seinem Gebiet führend, das bewährte Material der Vorgängerauflagen wurde übernommen

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probability and Statistical Models with Applications is a must read for probabilists and theoretical and applied statisticians.

An introduction to applied probability; Assessing significance in a fourfold table; Determining sample sizes needed to detect a difference between two proportions; How to randomize; Sampling method; The analysis of data from matched samples; The comparison of proportions from several independent samples; Combining evidence from fourfold tables; The effects of misclassification errors; The control of misclassification error; The measurement of interrater agreement; The standardization of rates.

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.

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Since the original publication of the bestselling Modelling Binary Data, a number of important methodological and computational developments have emerged, accompanied by the steady growth of statistical computing. Mixed models for binary data analysis and procedures that lead to an exact version of logistic regression form valuable additions to the statistician's toolbox, and author Dave Collett has fully updated his popular treatise to incorporate these important advances. Modelling Binary Data, Second Edition now provides an even more comprehensive and practical guide to statistical methods for analyzing binary data. Along with thorough revisions to the original material-now independent of any particular software package- it includes a new chapter introducing mixed models for binary data analysis and another on exact methods for modelling binary data. The author has also added material on modelling ordered categorical data and provides a summary of the leading software packages. All of the data sets used in the book are available for download from the Internet, and the appendices include additional data sets useful as exercises.

This book is an interpretative presentation of the mathematical and logical basis of probability and statistics, indulging in some mathematics, but concentrating on the logical and scientific meaning of probability and statistical reasoning.