Blog Archives

Interpreting Bayesian posterior distribution of a parameter: Is density meaningful?

February 19, 2017
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Interpreting Bayesian posterior distribution of a parameter: Is density meaningful?

Background: Suppose a researcher is interested in the Bayesian posterior distribution of a parameter, because the parameter is directly meaningful in the research domain. This occurs, for example, in psychometrics. Specifically, in item response theory...

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Equivalence testing (two one-sided test) and NHST compared with HDI and ROPE

February 16, 2017
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Equivalence testing (two one-sided test) and NHST compared with HDI and ROPE

In this blog post I show that frequentist equivalence testing (using the procedure of two one-sided tests: TOST) with null hypothesis significance testing (NHST) can produce conflicting decisions for the same parameter values, that is, TOST can accept ...

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The Bayesian New Statistics – finally published

February 8, 2017
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The Bayesian New Statistics – finally published

The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective.Abstract: In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and es...

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Courses doing Bayesian data analysis, June 2017

January 29, 2017
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Courses doing Bayesian data analysis, June 2017

Choose from two multi-day workshops doing Bayesian data analysis in June, 2017:2017 June 20 - 23. Four-day course. Interuniversity Consortium for Political and Social Research (ICPSR), Ann Arbor, Michigan. 2017 June 5 - 9. Five-day course. Stats Camp, ...

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Bayesian assessment of null values

December 21, 2016
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Bayesian assessment of null values

A blog post by Christian Robert considered an ancient (2011!) article titled "Bayesian assessment of null values via parameter estimation and model comparison." Here I'll try to clarify the ideas from way back then through the lens of more recent diagr...

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The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective

December 16, 2016
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The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective

UPDATE: Now published, see this post.Two conceptual distinctions in the practice of data analysis. Rows show point-value hypothesis testing versus estimating magnitude with uncertainty. Columns show frequentist versus Bayesian methods. Cells indicate t...

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Is it legitimate to view the data and then decide on a distribution for the dependent variable?

November 17, 2016
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An emailer asks, In Bayesian parameter estimation, is it legitimate to view the data and then decide on a distribution for the dependent variable? I have heard that this is not “fully Bayesian”. The shortest questions often probe some of the most d...

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Bayesian meta-analysis of two proportions in random control trials

November 3, 2016
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Bayesian meta-analysis of two proportions in random control trials

For an article that's accepted pending final revision (available here at OSF), I developed a Bayesian meta-analysis of two proportions in random control trials. This blog post summarizes and links to the complete R scripts.We consider scenarios in whic...

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Should researchers be correcting for multiple tests, even when they themselves did not run the tests, but all of the tests were run on the same data?

October 25, 2016
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A graduate student, named Caitlin Ducate, in my frequentist statistics class asks:In Criminal Justice, it's common to use large data sets like the Uniform Crime Report (UCR) or versions of the National Longitudinal Survey (NLS) because the nature of ...

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Posterior predictive distribution for multiple linear regression

October 22, 2016
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Suppose you've done a (robust) Bayesian multiple linear regression, and now you want the posterior distribution on the predicted value of \(y\) for some probe value of \( \langle x_1,x_2,x_3, ... \rangle \). That is, not the posterior distribution on t...

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