Bayesian Statistics for Experimental Scientists

Bayesian Statistics for Experimental Scientists

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  • Author: Richard A. Chechile
  • Publisher: MIT Press
  • ISBN: 0262360705
  • Category : Mathematics
  • Languages : en
  • Pages : 473

An introduction to the Bayesian approach to statistical inference that demonstrates its superiority to orthodox frequentist statistical analysis. This book offers an introduction to the Bayesian approach to statistical inference, with a focus on nonparametric and distribution-free methods. It covers not only well-developed methods for doing Bayesian statistics but also novel tools that enable Bayesian statistical analyses for cases that previously did not have a full Bayesian solution. The book's premise is that there are fundamental problems with orthodox frequentist statistical analyses that distort the scientific process. Side-by-side comparisons of Bayesian and frequentist methods illustrate the mismatch between the needs of experimental scientists in making inferences from data and the properties of the standard tools of classical statistics.


The Subjectivity of Scientists and the Bayesian Approach

The Subjectivity of Scientists and the Bayesian Approach

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  • Author: S. James Press
  • Publisher: Courier Dover Publications
  • ISBN: 0486810453
  • Category : Mathematics
  • Languages : en
  • Pages : 288

Intriguing examination of works by Aristotle, Galileo, Newton, Pasteur, Einstein, Margaret Mead, and other scientists in terms of subjectivity and the Bayesian approach to statistical analysis. "An insightful work." — Choice. 2001 edition.


Doing Bayesian Data Analysis

Doing Bayesian Data Analysis

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  • Author: John Kruschke
  • Publisher: Academic Press
  • ISBN: 0123814863
  • Category : Mathematics
  • Languages : en
  • Pages : 673

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and BUGS 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 BUGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment


The Nature of Scientific Evidence

The Nature of Scientific Evidence

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  • Author: Mark L. Taper
  • Publisher: University of Chicago Press
  • ISBN: 0226789586
  • Category : Science
  • Languages : en
  • Pages : 448

An exploration of the statistical foundations of scientific inference, The Nature of Scientific Evidence asks what constitutes scientific evidence and whether scientific evidence can be quantified statistically. Mark Taper, Subhash Lele, and an esteemed group of contributors explore the relationships among hypotheses, models, data, and inference on which scientific progress rests in an attempt to develop a new quantitative framework for evidence. Informed by interdisciplinary discussions among scientists, philosophers, and statisticians, they propose a new "evidential" approach, which may be more in keeping with the scientific method. The Nature of Scientific Evidence persuasively argues that all scientists should care more about the fine points of statistical philosophy because therein lies the connection between theory and data. Though the book uses ecology as an exemplary science, the interdisciplinary evaluation of the use of statistics in empirical research will be of interest to any reader engaged in the quantification and evaluation of data.


Bayesian Reasoning in Data Analysis

Bayesian Reasoning in Data Analysis

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  • Author: Giulio D'Agostini
  • Publisher: World Scientific
  • ISBN: 9814486094
  • Category : Mathematics
  • Languages : en
  • Pages : 352

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


Introduction to Bayesian Statistics

Introduction to Bayesian Statistics

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  • Author: William M. Bolstad
  • Publisher: John Wiley & Sons
  • ISBN: 1118091566
  • Category : Mathematics
  • Languages : en
  • Pages : 617

"...this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible. It is both concise and timely, and provides a good collection of overviews and reviews of important tools used in Bayesian statistical methods." There is a strong upsurge in the use of Bayesian methods in applied statistical analysis, yet most introductory statistics texts only present frequentist methods. Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. The authors continue to provide a Bayesian treatment of introductory statistical topics, such as scientific data gathering, discrete random variables, robust Bayesian methods, and Bayesian approaches to inference for discrete random variables, binomial proportions, Poisson, and normal means, and simple linear regression. In addition, more advanced topics in the field are presented in four new chapters: Bayesian inference for a normal with unknown mean and variance; Bayesian inference for a Multivariate Normal mean vector; Bayesian inference for the Multiple Linear Regression Model; and Computational Bayesian Statistics including Markov Chain Monte Carlo. The inclusion of these topics will facilitate readers' ability to advance from a minimal understanding of Statistics to the ability to tackle topics in more applied, advanced level books. Minitab macros and R functions are available on the book's related website to assist with chapter exercises. Introduction to Bayesian Statistics, Third Edition also features: Topics including the Joint Likelihood function and inference using independent Jeffreys priors and join conjugate prior The cutting-edge topic of computational Bayesian Statistics in a new chapter, with a unique focus on Markov Chain Monte Carlo methods Exercises throughout the book that have been updated to reflect new applications and the latest software applications Detailed appendices that guide readers through the use of R and Minitab software for Bayesian analysis and Monte Carlo simulations, with all related macros available on the book's website Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics.


Bayesian Statistics for Social Scientists

Bayesian Statistics for Social Scientists

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  • Author: Lawrence D. Phillips
  • Publisher:
  • ISBN:
  • Category : Bayesian statistical decision theory
  • Languages : en
  • Pages : 472


Scientific Reasoning

Scientific Reasoning

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  • Author: Colin Howson
  • Publisher:
  • ISBN:
  • Category : Bayesian statistical decision theory
  • Languages : en
  • Pages : 504

"Scientific Reasoning: The Bayesian Approach explains, in an accessible style, those elements of the probability calculus that are relevant to Bayesian methods, and argues that the probability calculus is best regarded as a species of logic." "Howson and Urbach contrast the Bayesian with the 'classical' view that was so influential in the last century, and demonstrate that familiar classical procedures for evaluating statistical hypotheses, such as significance tests, point estimation, confidence intervals, and other techniques, provide an utterly false basis for scientific inference. They also expose the well-known non-probabilistic philosophies of Popper, Lakatos, and Kuhn as similarly unscientific." "Scientific Reasoning shows how Bayesian theory, by contrast with these increasingly discredited approaches, provides a unified and highly satisfactory account of scientific method, an account which practicing scientists and all those interested in the sciences ought to master."--BOOK JACKET.


Bayesian Statistics for the Social Sciences

Bayesian Statistics for the Social Sciences

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  • Author: David Kaplan
  • Publisher: Guilford Publications
  • ISBN: 1462553540
  • Category : Business & Economics
  • Languages : en
  • Pages : 274

"Since the publication of the first edition, Bayesian statistics is, arguably, still not the norm in the formal quantitative methods training of social scientists. Typically, the only introduction that a student might have to Bayesian ideas is a brief overview of Bayes' theorem while studying probability in an introductory statistics class. This is not surprising. First, until relatively recently, it was not feasible to conduct statistical modeling from a Bayesian perspective owing to its complexity and lack of available software. Second, Bayesian statistics represents a powerful alternative to frequentist (conventional) statistics and, therefore, can be controversial, especially in the context of null hypothesis significance testing. However, over the last 20 years, or so, considerably progress has been made in the development and application of complex Bayesian statistical methods, due mostly to developments and availability of proprietary and open-source statistical software tools. And, although Bayesian statistics is not quite yet an integral part of the quantitative training of social scientists, there has been increasing interest in the application of Bayesian methods, and it is not unreasonable to say that in terms of theoretical developments and substantive applications, Bayesian statistics has arrived. Because of extensive developments in Bayesian theory and computation since the publication of the first edition of this book, there was a pressing need for a thorough update of the material to reflect new developments in Bayesian methodology and software. The basic foundations of Bayesian statistics remain more or less the same, but this second edition encompasses many new extensions"--


Error and the Growth of Experimental Knowledge

Error and the Growth of Experimental Knowledge

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  • Author: Deborah G. Mayo
  • Publisher: University of Chicago Press
  • ISBN: 0226511995
  • Category : Science
  • Languages : en
  • Pages : 512

We may learn from our mistakes, but Deborah Mayo argues that, where experimental knowledge is concerned, we haven't begun to learn enough. Error and the Growth of Experimental Knowledge launches a vigorous critique of the subjective Bayesian view of statistical inference, and proposes Mayo's own error-statistical approach as a more robust framework for the epistemology of experiment. Mayo genuinely addresses the needs of researchers who work with statistical analysis, and simultaneously engages the basic philosophical problems of objectivity and rationality. Mayo has long argued for an account of learning from error that goes far beyond detecting logical inconsistencies. In this book, she presents her complete program for how we learn about the world by being "shrewd inquisitors of error, white gloves off." Her tough, practical approach will be important to philosophers, historians, and sociologists of science, and will be welcomed by researchers in the physical, biological, and social sciences whose work depends upon statistical analysis.