A Galton Board Demonstration of Why All Statistical Models are Misspecified

The Galton board or quincunx is a fascinating device that provides a compelling demonstration of one the main laws of statistics. In the device, balls are dropped from above onto a series of pegs that are organized in rows of increasing width. Whenever a ball hits a particular peg, it can drop either to the right or to the left,…

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The Single Most Prevalent Misinterpretation of Bayes’ Rule

We thank Alexander Ly for constructive comments on an earlier draft of this post. Bayes’ rule tells us how to learn from experience, that is, by updating our knowledge about the world using relative predictive performance: hypotheses that predicted the data relatively well receive a boost in credibility, whereas hypotheses that predicted the data relatively poorly suffer a decline (e.g.,…

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Preprint: Multiple Perspectives on Inference for Two Simple Statistical Scenarios

Abstract When data analysts operate within different statistical frameworks (e.g., frequentist versus Bayesian, emphasis on estimation versus emphasis on testing), how does this impact the qualitative conclusions that are drawn for real data? To study this question empirically we selected from the literature two simple scenarios -involving a comparison of two proportions and a Pearson correlation- and asked four teams…

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Rejoinder: More Limitations of Bayesian Leave-One-Out Cross-Validation

In a recent article for Computational Brain & Behavior, we discussed several limitations of Bayesian leave-one-out cross-validation (LOO) for model selection. Our contribution attracted three thought-provoking commentaries by (1) Vehtari, Simpson, Yao, and Gelman, (2) Navarro, and (3) Shiffrin and Chandramouli. We just submitted a rejoinder in which we address each of the commentaries and identify several additional limitations of…

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