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

Bayesian Data Analysis, Third Edition

Bayesian Data Analysis, Third Edition
Author: Andrew Gelman
Publisher: CRC Press
Total Pages: 677
Release: 2013-11-01
Genre: Mathematics
ISBN: 1439840954

Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Bayesian Inference in Statistical Analysis

Bayesian Inference in Statistical Analysis
Author: George E. P. Box
Publisher: John Wiley & Sons
Total Pages: 610
Release: 2011-01-25
Genre: Mathematics
ISBN: 111803144X

Its main objective is to examine the application and relevance of Bayes' theorem to problems that arise in scientific investigation in which inferences must be made regarding parameter values about which little is known a priori. Begins with a discussion of some important general aspects of the Bayesian approach such as the choice of prior distribution, particularly noninformative prior distribution, the problem of nuisance parameters and the role of sufficient statistics, followed by many standard problems concerned with the comparison of location and scale parameters. The main thrust is an investigation of questions with appropriate analysis of mathematical results which are illustrated with numerical examples, providing evidence of the value of the Bayesian approach.

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.

Statistical Inference in Science

Statistical Inference in Science
Author: D.A. Sprott
Publisher: Springer Science & Business Media
Total Pages: 254
Release: 2008-01-28
Genre: Mathematics
ISBN: 0387227660

A treatment of the problems of inference associated with experiments in science, with the emphasis on techniques for dividing the sample information into various parts, such that the diverse problems of inference that arise from repeatable experiments may be addressed. A particularly valuable feature is the large number of practical examples, many of which use data taken from experiments published in various scientific journals. This book evolved from the authors own courses on statistical inference, and assumes an introductory course in probability, including the calculation and manipulation of probability functions and density functions, transformation of variables and the use of Jacobians. While this is a suitable text book for advanced undergraduate, Masters, and Ph.D. statistics students, it may also be used as a reference book.

Philosophical Problems of Statistical Inference

Philosophical Problems of Statistical Inference
Author: T. Seidenfeld
Publisher: Springer Science & Business Media
Total Pages: 274
Release: 1979-08-31
Genre: Social Science
ISBN: 9789027709653

Probability and inverse inference; Neyman-Pearson theory; Fisherian significance testing; The fiducial argument: one parameter; The fiducial argument: several parameters; Ian hacking's theory; Henry Kyburg's theory; Relevance and experimental design.

Bayesian Logical Data Analysis for the Physical Sciences

Bayesian Logical Data Analysis for the Physical Sciences
Author: Phil Gregory
Publisher: Cambridge University Press
Total Pages: 498
Release: 2005-04-14
Genre: Mathematics
ISBN: 113944428X

Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.

Tools for Statistical Inference

Tools for Statistical Inference
Author: Martin A. Tanner
Publisher: Springer Science & Business Media
Total Pages: 215
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461240247

A unified introduction to a variety of computational algorithms for likelihood and Bayesian inference. This third edition expands the discussion of many of the techniques presented, and includes additional examples as well as exercise sets at the end of each chapter.

Bayesian Theory and Applications

Bayesian Theory and Applications
Author: Paul Damien
Publisher: Oxford University Press
Total Pages: 717
Release: 2013-01-24
Genre: Mathematics
ISBN: 0199695601

This volume guides the reader along a statistical journey that begins with the basic structure of Bayesian theory, and then provides details on most of the past and present advances in this field.