Inferential Models

Inferential Models
Author: Ryan Martin
Publisher: CRC Press
Total Pages: 274
Release: 2015-09-25
Genre: Mathematics
ISBN: 1439886512

A New Approach to Sound Statistical ReasoningInferential Models: Reasoning with Uncertainty introduces the authors' recently developed approach to inference: the inferential model (IM) framework. This logical framework for exact probabilistic inference does not require the user to input prior information. The authors show how an IM produces meaning

Exact Statistical Methods for Data Analysis

Exact Statistical Methods for Data Analysis
Author: Samaradasa Weerahandi
Publisher: Springer Science & Business Media
Total Pages: 343
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461208254

Now available in paperback, this book covers some recent developments in statistical inference. It provides methods applicable in problems involving nuisance parameters such as those encountered in comparing two exponential distributions or in ANOVA without the assumption of equal error variances. The generalized procedures are shown to be more powerful in detecting significant experimental results and in avoiding misleading conclusions.

R.A. Fisher: An Appreciation

R.A. Fisher: An Appreciation
Author: Stephen E. Fienberg
Publisher: Springer Science & Business Media
Total Pages: 219
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461260795

From the reviews: "This collection of essays surveys the most important of Fisher's papers in various areas of statistics. ... ... the monograph will be a useful source of reference to most of Fisher's major papers; it will certainly provide background material for much vigorous discussion." #Australian Journal of Statistics#1

Fisher, Neyman, and the Creation of Classical Statistics

Fisher, Neyman, and the Creation of Classical Statistics
Author: Erich L. Lehmann
Publisher: Springer Science & Business Media
Total Pages: 123
Release: 2011-07-25
Genre: Mathematics
ISBN: 1441995005

Classical statistical theory—hypothesis testing, estimation, and the design of experiments and sample surveys—is mainly the creation of two men: Ronald A. Fisher (1890-1962) and Jerzy Neyman (1894-1981). Their contributions sometimes complemented each other, sometimes occurred in parallel, and, particularly at later stages, often were in strong opposition. The two men would not be pleased to see their names linked in this way, since throughout most of their working lives they detested each other. Nevertheless, they worked on the same problems, and through their combined efforts created a new discipline. This new book by E.L. Lehmann, himself a student of Neyman’s, explores the relationship between Neyman and Fisher, as well as their interactions with other influential statisticians, and the statistical history they helped create together. Lehmann uses direct correspondence and original papers to recreate an historical account of the creation of the Neyman-Pearson Theory as well as Fisher’s dissent, and other important statistical theories.

A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem

A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem
Author: Tejas Desai
Publisher: Springer Science & Business Media
Total Pages: 60
Release: 2013-02-26
Genre: Mathematics
ISBN: 1461464439

​​ ​ In statistics, the Behrens–Fisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an approach to the Behrens-Fisher problem. Since high-speed computers were not available in Fisher’s time, this approach was not implementable and was soon forgotten. Fortunately, now that high-speed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fisher’s approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case. In this monograph, we present the solution to the afore-mentioned multivariate generalization of the Behrens-Fisher problem. We start out by presenting a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate Behrens-Fisher problem. All methods proposed in this monograph will be include both the randomly-incomplete-data case as well as the complete-data case. Moreover, all methods considered in this monograph will be tested using both simulations and examples. ​

Encyclopedia of Research Design

Encyclopedia of Research Design
Author: Neil J. Salkind
Publisher: SAGE
Total Pages: 1779
Release: 2010-06-22
Genre: Philosophy
ISBN: 1412961270

"Comprising more than 500 entries, the Encyclopedia of Research Design explains how to make decisions about research design, undertake research projects in an ethical manner, interpret and draw valid inferences from data, and evaluate experiment design strategies and results. Two additional features carry this encyclopedia far above other works in the field: bibliographic entries devoted to significant articles in the history of research design and reviews of contemporary tools, such as software and statistical procedures, used to analyze results. It covers the spectrum of research design strategies, from material presented in introductory classes to topics necessary in graduate research; it addresses cross- and multidisciplinary research needs, with many examples drawn from the social and behavioral sciences, neurosciences, and biomedical and life sciences; it provides summaries of advantages and disadvantages of often-used strategies; and it uses hundreds of sample tables, figures, and equations based on real-life cases."--Publisher's description.

Theory of U-Statistics

Theory of U-Statistics
Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
Total Pages: 558
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401735158

The theory of U-statistics goes back to the fundamental work of Hoeffding [1], in which he proved the central limit theorem. During last forty years the interest to this class of random variables has been permanently increasing, and thus, the new intensively developing branch of probability theory has been formed. The U-statistics are one of the universal objects of the modem probability theory of summation. On the one hand, they are more complicated "algebraically" than sums of independent random variables and vectors, and on the other hand, they contain essential elements of dependence which display themselves in the martingale properties. In addition, the U -statistics as an object of mathematical statistics occupy one of the central places in statistical problems. The development of the theory of U-statistics is stipulated by the influence of the classical theory of summation of independent random variables: The law of large num bers, central limit theorem, invariance principle, and the law of the iterated logarithm we re proved, the estimates of convergence rate were obtained, etc.

Bayesian Statistics

Bayesian Statistics
Author: Peter M. Lee
Publisher: Wiley
Total Pages: 352
Release: 2009-01-20
Genre: Mathematics
ISBN: 9780340814055

Bayesian Statistics is the school of thought that uses all information surrounding the likelihood of an event rather than just that collected experimentally. Among statisticians the Bayesian approach continues to gain adherents and this new edition of Peter Lee’s well-established introduction maintains the clarity of exposition and use of examples for which this text is known and praised. In addition, there is extended coverage of the Metropolis-Hastings algorithm as well as an introduction to the use of BUGS (Bayesian Inference Using Gibbs Sampling) as this is now the standard computational tool for such numerical work. Other alterations include new material on generalized linear modelling and Bernardo’s theory of reference points.

Aspects of Multivariate Statistical Theory

Aspects of Multivariate Statistical Theory
Author: Robb J. Muirhead
Publisher: John Wiley & Sons
Total Pages: 706
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470316705

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . . the wealth of material on statistics concerning the multivariate normal distribution is quite exceptional. As such it is a very useful source of information for the general statistician and a must for anyone wanting to penetrate deeper into the multivariate field." -Mededelingen van het Wiskundig Genootschap "This book is a comprehensive and clearly written text on multivariate analysis from a theoretical point of view." -The Statistician Aspects of Multivariate Statistical Theory presents a classical mathematical treatment of the techniques, distributions, and inferences based on multivariate normal distribution. Noncentral distribution theory, decision theoretic estimation of the parameters of a multivariate normal distribution, and the uses of spherical and elliptical distributions in multivariate analysis are introduced. Advances in multivariate analysis are discussed, including decision theory and robustness. The book also includes tables of percentage points of many of the standard likelihood statistics used in multivariate statistical procedures. This definitive resource provides in-depth discussion of the multivariate field and serves admirably as both a textbook and reference.

Exploratory Data Analysis Using Fisher Information

Exploratory Data Analysis Using Fisher Information
Author: Roy Frieden
Publisher: Springer Science & Business Media
Total Pages: 375
Release: 2010-05-27
Genre: Computers
ISBN: 1846287774

This book uses a mathematical approach to deriving the laws of science and technology, based upon the concept of Fisher information. The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). The authors show how to use EPI to determine the theoretical input/output laws of unknown systems. Will benefit readers whose math skill is at the level of an undergraduate science or engineering degree.