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

Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.
This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis,...

Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation.

The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the...

Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models.

Key features:

• Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment.
• Provides a thorough introduction for research students.
• Computational tools...

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers-in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible.

Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster...

Bayesian methods are a powerful tool in many areas of science and engineering, especially statistical physics, medical sciences, electrical engineering, and information sciences. They are also ideal for civil engineering applications, given the numerous types of modeling and parametric uncertainty in civil engineering problems. For example, earthquake ground motion cannot be predetermined at the structural design stage. Complete wind pressure profiles are difficult to measure under operating conditions. Material properties can be difficult to determine to a very precise level - especially...

Though there are many recent additions to graduate-level introductory books on Bayesian analysis, none has quite our blend of theory, methods, and ap- plications. We believe a beginning graduate student taking a Bayesian course or just trying to find out what it means to be a Bayesian ought to have some familiarity with all three aspects. More specialization can come later. Each of us has taught a course like this at Indian Statistical Institute or Purdue. In fact, at least partly, the book grew out of those courses. We would also like to refer to the review (Ghosh and Samanta (2002b)) that...

Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods.

The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models...

This popular problem collection is now available in paperback to be used for self study and in conjunction with basic courses in probability and statistics. Its strength lies in the originality of the problems which have been extensively tested in teaching by the author and others.

1. A self-contained introduction to probability, exchangeability and Bayes rule provides a theoretical understanding of the applied material.

2. Numerous examples with R-code that can be run "as-is" allow the reader to perform the data analyses themselves.

3. The development of Monte Carlo and Markov chain Monte Carlo methods in the context of data analysis examples provides motivation for these computational methods.

"

This volume consists of a collection of research articles on classical and emerging Statistical Paradigms parametric, non-parametric and semi-parametric, frequentist and Bayesian encompassing both theoretical advances and emerging applications in a variety of scientific disciplines. For advances in theory, the topics include: Bayesian Inference, Directional Data Analysis, Distribution Theory, Econometrics and Multiple Testing Procedures. The areas in emerging applications include: Bioinformatics, Factorial Experiments and Linear Models, Hotspot Geoinformatics and Reliability.

This book, written by two mathematicians from the University of Southern California, provides a broad introduction to the important subject of nonlinear mixture models from a Bayesian perspective. It contains background material, a brief description of Markov chain theory, as well as novel algorithms and their applications. It is self-contained and unified in presentation, which makes it ideal for use as an advanced textbook by graduate students and as a reference for independent researchers. The explanations in the book are detailed enough to capture the interest of the curious reader, and...

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probability. The theory draws on the work of A. P. Dempster but diverges from Depster's viewpoint by identifying his "lower probabilities" as epistemic probabilities and taking his rule for combining "upper and lower probabilities" as fundamental.

The book opens with a critique of the well-known Bayesian theory of epistemic probability. It then proceeds...

Following in the footsteps of its bestselling predecessors, the Handbook of Parametric and Nonparametric Statistical Procedures, Fifth Edition provides researchers, teachers, and students with an all-inclusive reference on univariate, bivariate, and multivariate statistical procedures.

New in the Fifth Edition:

• Substantial updates and new material throughout
• New chapters on path analysis, meta-analysis, and structural equation modeling
• Index numbers and time series...

Most introductory statistics text-books are written either in a highly mathematical style for an intended readership of mathematics undergraduate students, or in a recipe-book style for an intended audience of non-mathematically inclined undergraduate or postgraduate students, typically in a single discipline; hence, "statistics for biologists," "statistics for psychologists," and so on.
An antidote to technique-oriented service courses, Statistics and Scientific Method is different. It studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to...

Together with the fundamentals of probability, random processes, and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Ito process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum-Welch algorithms, algorithms for machine learning, Wiener and Kalman...

This book begins the task of defining, explaining, arguing for, and, in the end, providing a rationale for information processing. Volume I is concerned with the notion that an information processor is mainly engaged in making inferences. An information processor would prefer to reach definite conclusions by using some form of deduction. Unfortunately, it is often thwarted in this desire by a fundamental lack of relevant information. Probability theory has developed as a rigorous way of dealing with the uncertainty surrounding inference. Thus, we begin by treating some of the formal...

The Valencia International Meetings on Bayesian Statistics - established in 1979 and held every four years - have been the forum for a definitive overview of current concerns and activities in Bayesian statistics. These are the edited Proceedings of the Ninth meeting, and contain the invited papers each followed by their discussion and a rejoinder by the authors(s). In the tradition of the earlier editions, this encompasses an enormous range of theoretical and applied research, high lighting the breadth, vitality and impact of Bayesian thinking in interdisciplinary research across many fields...

Bayesian Statistics is the school of thought that combines prior beliefs with the likelihood of a hypothesis to arrive at posterior beliefs. The first edition of Peter Lee's book appeared in 1989, but the subject has moved ever onwards, with increasing emphasis on Monte Carlo based techniques.

This new fourth edition looks at recent techniques such as variational methods, Bayesian importance sampling, approximate Bayesian computation and Reversible Jump Markov Chain Monte Carlo (RJMCMC), providing a concise account of the way in which the Bayesian approach to statistics develops as...

A practical approach to estimating and tracking dynamic systems in real-worl applications

Much of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by Gaussian and non-Gaussian noices.

Featuring a unified approach to Bayesian estimation and tracking, the...

Written with students and professors in mind, Analysis of Queues: Methods and Applications combines coverage of classical queueing theory with recent advances in studying stochastic networks. Exploring a broad range of applications, the book contains plenty of solved problems, exercises, case studies, paradoxes, and numerical examples.

In addition to the standard single-station and single class discrete queues, the book discusses models for multi-class queues and queueing networks as well as methods based on fluid scaling, stochastic fluid flows, continuous...