Kategoria BISAC: Mathematics >> Probability & Statistics - Bayesian Analysis

Topics treated in this text fall into three main groups, all of which deal with classical problems which originated in the work of Kolmogorov. The first section looks at probability limit theorems, the second deals with stochastic analysis, and the final part presents some papers on nonparametric and semiparametric models of mathematical statistics and asymptotic problems. The contributions come from some of the foremost mathematicians in the world today, making for an international collection of papers, permeated with the influence of Kolmogorov's works.

A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout.
The author presents classical results and methods that form the basis of modern statistics, and examines the foundations of estimation theory, hypothesis testing theory and statistical game theory. He then considers statistical problems for two or more samples, and those in which observations are taken from different distributions. Methods of finding optimal and...

This book is the sixth edition of a classic text that was first published in 1950 in the former Soviet Union. The clear presentation of the subject and extensive applications supported with real data helped establish the book as a standard for the field. To date, it has been published into more that ten languages and has gone through five editions.
The sixth edition is a major revision over the fifth. It contains new material and results on the Local Limit Theorem, the Integral Law of Large Numbers, and Characteristic Functions. The new edition retains the feature of developing the...

This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and...

This textbook is related to a course that the author taught for many years at University of California, Berkeley. The course was originally intended for graduate students in the biological and health sciences. But it attracted students from other departments on the campus as well. In order for the book to serve the interest of a larger audience, the author made revisions of the outline, added new topics, and provided more examples for illustrations wherever needed.

This invaluable book systematically presents fundamental methods of statistical analysis: from basic probability and...

This textbook is related to a course that the author taught for many years at University of California, Berkeley. The course was originally intended for graduate students in the biological and health sciences. But it attracted students from other departments on the campus as well. In order for the book to serve the interest of a larger audience, the author made revisions of the outline, added new topics, and provided more examples for illustrations wherever needed.

This invaluable book systematically presents fundamental methods of statistical analysis: from basic probability and...

This book provides a multi-level introduction to Bayesian reasoning (as opposed to "conventional statistics") and its applications to data analysis. The basic ideas of this "new" approach to the quantification of uncertainty are presented using examples from research and everyday life. Applications covered include: parametric inference; combination of results; treatment of uncertainty due to systematic errors and background; comparison of hypotheses; unfolding of experimental distributions; upper/lower bounds in frontier-type measurements. Approximate methods for routine use are derived and...

This book encompasses a wide range of important topics. The articles cover the following areas: asymptotic theory and inference, biostatistics, economics and finance, statistical computing and Bayesian statistics, and statistical genetics. Specifically, the issues that are studied include large deviation, deviation inequalities, local sensitivity of model misspecification in likelihood inference, empirical likelihood confidence intervals, uniform convergence rates in density estimation, randomized designs in clinical trials, MCMC and EM algorithms, approximation of p-values in multipoint...

Contains contributions from many of the mathematicians at the forefront of this effort.

Markov Chain Monte Carlo (MCMC) originated in statistical physics, but has spilled over into various application areas, leading to a corresponding variety of techniques and methods. That variety stimulates new ideas and developments from many different places, and there is much to be gained from cross-fertilization. This book presents five expository essays by leaders in the field, drawing from perspectives in physics, statistics and genetics, and showing how different aspects of MCMC come to the fore in different contexts. The essays derive from tutorial lectures at an interdisciplinary...

This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

'Bayesian Belief Networks' presents: 1. An introduction to and definition of BBNs. 2. Step-by-step practical guidelines to applying BBNs. 3. A wide variety of applications in industry, natural sciences, services and computing. 4. A discussion of the future directions BBN research and applications might take.

In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the random analog of the Prohorov theorem, which is obtained without invoking an embedding of the Polish space into a compact space. Further, the narrow topology is examined and other natural topologies on random measures are compared. In addition, it is...

Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors. The methods are based on the inverse Bayes formulae discovered by one of the author in 1995. Applying the Bayesian approach to important real-world problems, the authors focus on exact numerical solutions, a conditional sampling approach via data augmentation, and a noniterative sampling approach via EM-type algorithms.

After introducing the missing data...

Using WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, Bayesian Methods for Measures of Agreement presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process.

The author employs a Bayesian approach to provide statistical inferences based on various models of intra- and interrater agreement. He presents many examples that illustrate the Bayesian mode of reasoning and explains elements of a Bayesian application, including prior information,...

In many areas of applied statistics like economics or finance it is often desirable to find groups of similar time series in a set or panel of time series. Therefore, clustering techniques are required to determine subsets of similar time series. While distance-based clustering methods cannot easily be extended to time series data, model-based clustering based on finite mixture models extends to time series data in quite a natural way.
The author Christoph Pamminger proposes and discusses two approaches for model-based clustering methods specifically designed for categorical time series data...

This important book presents developments in a remarkable field of inquiry in statistical/probability theory — the stress-strength model.Many papers in the field include the enigmatic “words” P(X

Broadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (MCMC) methods and related data analytic techniques.

New to the Third Edition

New data examples, corresponding R and WinBUGS code, and homework problems

Explicit descriptions and...

Integrating interesting and widely used concepts of financial engineering into traditional statistics courses, Introduction to Probability and Statistics for Science, Engineering, and Finance illustrates the role and scope of statistics and probability in various fields. The text first introduces the basics needed to understand and create tables and graphs produced by standard statistical software packages, such as Minitab, SAS, and JMP. It then takes students through the traditional topics of a first course in statistics. Novel features include: Applications of standard statistical concepts...

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective.

Taking a clear, unified, and self-contained approach, the authors first develop the abstract general theory in the framework of weak solutions, before turning to cases of random and nonautonomous equations. They prove that time dependence and...