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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 of statisticians to provide a concise analysis and a qualitative interpretation of the outcome. The results showed considerable overall agreement; nevertheless, this agreement did not appear to diminish the intensity of the subsequent debate over which statistical framework is more appropriate to address the questions at hand.

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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 LOO-based methods such as Bayesian stacking. We focus on differences between LOO-based methods versus approaches that consistently use Bayes’ rule for both parameter estimation and model comparison.

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