Dr Quentin Gronau

Whenever someone in a team tries to help others, it is crucial that they have some understanding of other team members' goals. In modern teams, this applies equally to human and artificial ("bot") assistants. Understanding when one does not know something is crucial for stopping the execution of inappropriate behavior and, ideally, attempting to learn more appropriate actions. From a statistical point of view, this can be translated to assessing whether none of the hypotheses in a considered set is correct. Here we investigate a novel approach for making this assessment based on monitoring the maximum a posteriori probability (MAP) of a set of candidate hypotheses as new observations arrive. Simulation studies suggest that this is a promising approach, however, we also caution that there may be cases where this is more challenging. The problem we study and the solution we propose are general, with applications well beyond human¿bot teaming, including for example the scientific process of theory development.

After Bayes, the oldest Bayesian account of enumerative induction is given by Laplace's so-called rule of succession: if all n observed instances of a phenomenon to date exhibit a given character, the probability that the next instance of that phenomenon will also exhibit the character is (Formula presented). Laplace's rule however has the apparently counterintuitive mathematical consequence that the corresponding "universal generalization" (every future observation of this type will also exhibit that character) has zero probability. In 1932, the British scientist J. B. S. Haldane proposed an alternative rule giving a universal generalization the positive probability (Formula presented). A year later, Harold Jeffreys proposed essentially the same rule in the case of a finite population. A related variant rule results in a predictive probability of (Formula presented). These arguably elegant adjustments of the original Laplacean form have the advantage that they give predictions better aligned with intuition and common sense. In this paper, we discuss J. B. S. Haldane's rule and its variants, placing them in their historical context, and relating them to subsequent philosophical discussions.

Team-science projects have become the "gold standard" for assessing the replicability and variability of key findings in psychological science. However, we believe the typical meta-analytic approach in these projects fails to match the wealth of collected data. Instead, we advocate the use of Bayesian hierarchical modeling for team-science projects, potentially extended in a multiverse analysis. We illustrate this full-scale analysis by applying it to the recently published Many Labs 4 project. This project aimed to replicate the mortality-salience effect¿that being reminded of one's own death strengthens the own cultural identity. In a multiverse analysis, we assess the robustness of the results with varying data-inclusion criteria and prior settings. Bayesian model comparison results largely converge to a common conclusion: The data provide evidence against a mortality-salience effect across the majority of our analyses. We issue general recommendations to facilitate full-scale analyses in team-science projects.

van Doorn et al. (2021) outlined various questions that arise when conducting Bayesian model comparison for mixed effects models. Seven response articles offered their own perspective on the preferred setup for mixed model comparison, on the most appropriate specification of prior distributions, and on the desirability of default recommendations. This article presents a round-table discussion that aims to clarify outstanding issues, explore common ground, and outline practical considerations for any researcher wishing to conduct a Bayesian mixed effects model comparison.

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.