Doing Bayesian Data Analysis: A Tutorial with R and BUGS
TLDR
Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples.Abstract:
There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis obtainable to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS provides an accessible approach to Bayesian data analysis, as material is explained clearly with concrete examples. The book begins with the basics, including essential concepts of probability and random sampling, and gradually progresses to advanced hierarchical modeling methods for realistic data. The text delivers 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). This book is intended for first year graduate students or advanced undergraduates. It provides a bridge between undergraduate training and modern Bayesian methods for data analysis, which is becoming the accepted research standard. Prerequisite is knowledge of algebra and basic calculus. Author website: http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/ -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 accomplishmentread more
Citations
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Pattern Recognition and Machine Learning
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The New Statistics Why and How
TL;DR: An eight-step new-statistics strategy for research with integrity is described, which starts with formulation of research questions in estimation terms, has no place for NHST, and is aimed at building a cumulative quantitative discipline.
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Using Bayes to get the most out of non-significant results
TL;DR: It is argued Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches, and provides a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive.
Reliability Engineering and System Safety
TL;DR: In this paper, a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions is presented.
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Bayesian Estimation Supersedes the t Test
TL;DR: Bayesian estimation for 2 groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their Difference, and the normality of the data.
References
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Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
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Pattern Recognition and Machine Learning
TL;DR: Probability Distributions, linear models for Regression, Linear Models for Classification, Neural Networks, Graphical Models, Mixture Models and EM, Sampling Methods, Continuous Latent Variables, Sequential Data are studied.
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Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
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Bayesian Data Analysis
TL;DR: Detailed notes on Bayesian Computation Basics of Markov Chain Simulation, Regression Models, and Asymptotic Theorems are provided.
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A technique for the measurement of attitudes
TL;DR: The instrument to be described here is not, however, indirect in the usual sense of the word; it does not seek responses to items apparently unrelated to the attitudes investigated, and seeks to measure prejudice in a manner less direct than is true of the usual prejudice scale.