Doing Bayesian Data Analysis: A Tutorial with R and BUGS

By John K. Kruschke. 2010

611 citations recorded by the source corpus.

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 accomplishment

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9902a3dc5ccfaf8dd34c38caa5ae725e1d3e6551

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Citations in the corpus

Bayesian estimation supersedes the t test. (2013, methodology): “Then I will turn to general foundational issues that undermine the usefulness of NHST in any application.”
Estimating Fisheries Reference Points from Catch and Resilience (2017, background): “It can be argued that catch data are the main input of CMSY and that catch must therefore be treated as unknown when establishing priors (e.g. Kruschke 2011).”
On Using Bayesian Methods to Address Small Sample Problems (2016, background): “…Carlo (MCMC), which is becoming increasingly synonymous with Bayesian estimation in empirical studies, this means that the quality of inference is controlled not by sample size approaching infinity, but rather by the number of samples taken approaching infinity (Kruschke, 2010; Lee & Song, 2004).”
Quantum Models of Cognition and Decision (2012, methodology): “Then we can use a beta distribution B(a + 1, b + 1) with a, b positive integers and M = a + b to define the prior (Kruschke, 2010):”
Bayesian Versus Orthodox Statistics: Which Side Are You On? (2011, methodology): “(Note that I will not discuss confidence intervals and credibility intervals, the Bayesian equivalent to a confidence interval, in this article; see Dienes, 2008, and Kruschke 2010b, 2011, for detailed discussion and calculations.)”
Using Bayes to get the most out of non-significant results (2014, methodology): “…be considered to evaluate that hypothesis), so one can go directly to the theoretically relevant specific contrasts of interest (Dienes, 2011; for more extended discussion see Dienes, forthcoming; and Kruschke, 2010a for the use of hierarchical modeling for dealing with multiple comparisons).”
Bayesian Assessment of Null Values Via Parameter Estimation and Model Comparison (2011, positive): “We then simply examine the posterior distribution on the parameters and examine the relationship of a ROPE around a difference of zero to the HDI of the credible differences (e.g., Gelman, Hill, Yajima, in press; Kruschke, 2010b, 2011).”
Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan (2014, methodology): “For example, another way of using HDIs was described by Joseph, Wolfson, and du Berger (1995a, 1995b). They considered an “average length criterion,” which requires that the average HDI width, across repeated simulated data, does not exceed some maximal value L. There is no explicit mention of power”
The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective (2017, neutral): “(Bayes factors for the individual betablocker studies can be computed exactly using extensions of formulas described on pages 160 and 305 of Kruschke, 2011b.) What should be the publication status of indecisive studies?”
Rejecting or Accepting Parameter Values in Bayesian Estimation (2018, neutral): “This HDI+ROPE decision rule has been described in several previous publications (Kruschke, 2010, 2011a, 2011b, 2013, 2015; Kruschke, Aguinis, & Joo, 2012; Kruschke & Liddell, 2018a, 2018b; Kruschke & Vanpaemel, 2015).”
Bayesian structural equation modeling: a more flexible representation of substantive theory. (2012, background): “Gelman, Carlin, Stern, and Rubin (2004) provided a good general statistical description, whereas Kruschke (2010) and Lynch (2010) gave somewhat more introductory accounts.”
How Bayes factors change scientific practice (2016, background): “Gelman et al. (2013) and Kruschke (2010) describe how to set up hierarchical models whereby the posterior distributions of the means of different conditions is automatically influenced by the data from all conditions.”
Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses (2019, background): “N 0,10002( ) This completely noninformative prior places independent, diffuse normal priors on each parameter in the vector B (Gelman and Hill 2007, Kruschke 2010, Korner-Nievergelt et al.”
Replication, statistical consistency, and publication bias. (2013, methodology): “In many cases data collection is not based on a fixed sample size but on the availability of participants over a certain time frame (Kruschke, 2010a).”