Data Analysis

A Bayesian Tutorial

Author: Devinderjit Sivia,John Skilling

Publisher: Oxford University Press

ISBN: 0198568312

Category: Mathematics

Page: 246

View: 3776

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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, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimental design. The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called 'nested sampling'.
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Data Analysis

A Bayesian Tutorial

Author: D. S. Sivia

Publisher: Oxford University Press

ISBN: 9780198518891

Category: Science

Page: 189

View: 5943

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Statistics lectures have often been viewed with trepidation by engineering and science students taking an ancillary course in this subject. Whereas there are many texts showing "how" statistical methods are applied, few provide a clear explanation for non-statisticians of how the principlesof data analysis can be based on probability theory. Data Analysis: A Bayesian Tutorial provides such a text, putting emphasis as much on understanding "why" and "when" certain statistical procedures should be used as "how". This difference in approach makes the text ideal as a tutorial guide forsenior 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. With its central emphasis on a fewfundamental rules, this book takes the mystery out of statistics by providing a clear rationale for some of the most widely-used procedures.
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Doing Bayesian Data Analysis

A Tutorial with R, JAGS, and Stan

Author: John Kruschke

Publisher: Academic Press

ISBN: 0124059163

Category: Mathematics

Page: 776

View: 5989

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Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact high-level scripts that make it easy to run the programs on your own data sets. The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment. This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and JAGS software Comprehensive coverage of all scenarios addressed by non-Bayesian textbooks: t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis) Coverage of experiment planning R and JAGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs
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Bayesian Reasoning in Data Analysis

A Critical Introduction

Author: Giulio D'Agostini

Publisher: World Scientific

ISBN: 9814486094

Category: Mathematics

Page: 352

View: 6271

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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 are shown often to coincide — under well-defined assumptions! — with “standard” methods, which can therefore be seen as special cases of the more general Bayesian methods. In dealing with uncertainty in measurements, modern metrological ideas are utilized, including the ISO classification of uncertainty into type A and type B. These are shown to fit well into the Bayesian framework. Contents: Critical Review and Outline of the Bayesian Alternative:Uncertainty in Physics and the Usual Methods of Handling ItA Probabilistic Theory of Measurement UncertaintyA Bayesian Primer:Subjective Probability and Bayes' TheoremProbability Distributions (A Concise Reminder)Bayesian Inference of Continuous QuantitiesGaussian LikelihoodCounting ExperimentsBypassing Bayes' Theorem for Routine ApplicationsBayesian UnfoldingFurther Comments, Examples and Applications:Miscellanea on General Issues in Probability and InferenceCombination of Experimental Results: A Closer LookAsymmetric Uncertainties and Nonlinear PropagationWhich Priors for Frontier Physics?Conclusion:Conclusions and Bibliography Readership: Graduate students and researchers interested in probability and statistics and their applications in science, particularly the evaluation of uncertainty in measurements. Keywords:Probability;Bayesian Statistics;Error Theory;Measurement Uncertainty;MetrologyReviews:“… statistics textbooks must take seriously the need to teach the foundations of statistical reasoning from the beginning … D'Agostini's new book does this admirably, building an edifice of Bayesian statistical reasoning in the physical sciences on solid foundations.”Journal of the American Statistical Association
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Bayesian Logical Data Analysis for the Physical Sciences

A Comparative Approach with Mathematica® Support

Author: Phil Gregory

Publisher: Cambridge University Press

ISBN: 9780521841504

Category: Mathematics

Page: 468

View: 6441

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Increasingly, researchers in many branches of science are coming into contact with Bayesian statistics or Bayesian probability theory. This book provides a clear exposition of the underlying concepts with large numbers of worked examples and problem sets. The book also discusses numerical techniques for implementing the Bayesian calculations, including Markov Chain Monte-Carlo integration and linear and nonlinear least-squares analysis seen from a Bayesian pe rspective. Background material is provided in appendices and supporting Mathematica notebooks are available. Suitable for upper-undergraduates, graduate students, or any serious researcher in physical sciences or engineering.
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Data Analysis in Forensic Science

A Bayesian Decision Perspective

Author: Franco Taroni,Silvia Bozza,Alex Biedermann,Paolo Garbolino,Colin Aitken

Publisher: John Wiley & Sons

ISBN: 9780470665077

Category: Mathematics

Page: 388

View: 8370

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This is the first text to examine the use of statistical methods in forensic science and bayesian statistics in combination. The book is split into two parts: Part One concentrates on the philosophies of statistical inference. Chapter One examines the differences between the frequentist, the likelihood and the Bayesian perspectives, before Chapter Two explores the Bayesian decision-theoretic perspective further, and looks at the benefits it carries. Part Two then introduces the reader to the practical aspects involved: the application, interpretation, summary and presentation of data analyses are all examined from a Bayesian decision-theoretic perspective. A wide range of statistical methods, essential in the analysis of forensic scientific data is explored. These include the comparison of allele proportions in populations, the comparison of means, the choice of sampling size, and the discrimination of items of evidence of unknown origin into predefined populations. Throughout this practical appraisal there are a wide variety of examples taken from the routine work of forensic scientists. These applications are demonstrated in the ever-more popular R language. The reader is taken through these applied examples in a step-by-step approach, discussing the methods at each stage.
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Bayesian Analysis with Python

Introduction to statistical modeling and probabilistic programming using PyMC3 and ArviZ, 2nd Edition

Author: Osvaldo Martin

Publisher: Packt Publishing Ltd

ISBN: 1789349664

Category: Computers

Page: 356

View: 1619

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Bayesian modeling with PyMC3 and exploratory analysis of Bayesian models with ArviZ Key Features A step-by-step guide to conduct Bayesian data analyses using PyMC3 and ArviZ A modern, practical and computational approach to Bayesian statistical modeling A tutorial for Bayesian analysis and best practices with the help of sample problems and practice exercises. Book Description The second edition of Bayesian Analysis with Python is an introduction to the main concepts of applied Bayesian inference and its practical implementation in Python using PyMC3, a state-of-the-art probabilistic programming library, and ArviZ, a new library for exploratory analysis of Bayesian models. The main concepts of Bayesian statistics are covered using a practical and computational approach. Synthetic and real data sets are used to introduce several types of models, such as generalized linear models for regression and classification, mixture models, hierarchical models, and Gaussian processes, among others. By the end of the book, you will have a working knowledge of probabilistic modeling and you will be able to design and implement Bayesian models for your own data science problems. After reading the book you will be better prepared to delve into more advanced material or specialized statistical modeling if you need to. What you will learn Build probabilistic models using the Python library PyMC3 Analyze probabilistic models with the help of ArviZ Acquire the skills required to sanity check models and modify them if necessary Understand the advantages and caveats of hierarchical models Find out how different models can be used to answer different data analysis questions Compare models and choose between alternative ones Discover how different models are unified from a probabilistic perspective Think probabilistically and benefit from the flexibility of the Bayesian framework Who this book is for If you are a student, data scientist, researcher, or a developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory so no previous statistical knowledge is required, although some experience in using Python and NumPy is expected.
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Essential Mathematical Methods for the Physical Sciences

Author: K. F. Riley,M. P. Hobson

Publisher: Cambridge University Press

ISBN: 1139492942

Category: Science

Page: N.A

View: 7814

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The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over 300 worked examples show how to use the techniques and around 100 self-test questions in the footnotes act as checkpoints to build student confidence. Nearly 400 end-of-chapter problems combine ideas from the chapter to reinforce the concepts. Hints and outline answers to the odd-numbered problems are given at the end of each chapter, with fully-worked solutions to these problems given in the accompanying Student Solutions Manual. Fully-worked solutions to all problems, password-protected for instructors, are available at www.cambridge.org/essential.
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Quantitative Genetics in the Wild

Author: Anne Charmantier,Dany Garant,Loeske E. B. Kruuk

Publisher: OUP Oxford

ISBN: 0191655961

Category: Science

Page: 288

View: 4745

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Although the field of quantitative genetics - the study of the genetic basis of variation in quantitative characteristics such as body size, or reproductive success - is almost 100 years old, its application to the study of evolutionary processes in wild populations has expanded greatly over the last few decades. During this time, the use of 'wild quantitative genetics' has provided insights into a range of important questions in evolutionary ecology, ranging from studies conducting research in well-established fields such as life-history theory, behavioural ecology and sexual selection, to others addressing relatively new issues such as populations' responses to climate change or the process of senescence in natural environments. Across these fields, there is increasing appreciation of the need to quantify the genetic - rather than just the phenotypic - basis and diversity of key traits, the genetic basis of the associations between traits, and the interaction between these genetic effects and the environment. This research activity has been fuelled by methodological advances in both molecular genetics and statistics, as well as by exciting results emerging from laboratory studies of evolutionary quantitative genetics, and the increasing availability of suitable long-term datasets collected in natural populations, especially in animals. Quantitative Genetics in the Wild is the first book to synthesize the current level of knowledge in this exciting and rapidly-expanding area. This comprehensive volume also offers exciting perspectives for future studies in emerging areas, including the application of quantitative genetics to plants or arthropods, unraveling the molecular basis of variation in quantitative traits, or estimating non-additive genetic variance. Since this book deals with many fundamental questions in evolutionary ecology, it should be of interest to graduate, post-graduate students, and academics from a wide array of fields such as animal behaviour, ecology, evolution, and genetics.
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Bayes' Rule

A Tutorial Introduction to Bayesian Analysis

Author: James V. Stone

Publisher: Sebtel Press

ISBN: 0956372848

Category: Bayesian statistical decision theory

Page: 170

View: 5262

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In this richly illustrated book, a range of accessible examples are used to show how Bayes' rule is actually a natural consequence of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for the novice who wishes to become familiar with the basic principles of Bayesian analysis.
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