“Not Only Defended But Also Applied”: The Perceived Absurdity of Bayesian Inference

A tutorial on Bayesian multi-model linear regression with BAS and JASP

Linear regression analyses commonly involve two consecutive stages of statistical inquiry. In the first stage, a single ‘best’ model is defined by a specific selection of relevant predictors; in the second stage, the regression coefficients of the winning model are used for prediction and for inference concerning the importance of the predictors. However, such second-stage inference ignores the model uncertainty from the first stage, resulting in overconfident parameter estimates that generalize poorly. These drawbacks can be overcome by model averaging, a technique that retains all models for inference, weighting each model’s contribution by its posterior probability. Although conceptually straightforward, model averaging is rarely used in applied research, possibly due to the lack of easily accessible software. To bridge the gap between theory and practice, we provide a tutorial on linear regression using Bayesian model averaging in JASP, based on the BAS package in R. Firstly, we provide theoretical background on linear regression, Bayesian inference, and Bayesian model averaging. Secondly, we demonstrate the method on an example data set from the World Happiness Report. Lastly, we discuss limitations of model averaging and directions for dealing with violations of model assumptions.

No credible evidence for links between 2D:4D and COVID-19 outcomes: A probabilistic perspective on digit ratio, ACE variants, and national case fatalities

Research into COVID-19 susceptibility and outcomes are critical, but claims must be carefully evaluated to inform policy decisions. In a recent series of articles, Manning and Fink [1-3] use national-level data to describe associations between case-fatality ratios and male and female finger ratios (2D:4D), a suggested measure of prenatal androgen exposure, as well as angiotensin-converting enzyme (ACE) allele and genotype frequencies. The authors suggest that 2D:4D is linked with ACE variant prevalence, and that higher male 2D:4D is associated with higher case fatality ratios, and point to 2D:4D as a useful prognostic measure for COVID-19 susceptibility. A critical review and robust Bayesian analysis of the hypothesis is described here, finding no conclusive evidence of COVID-19 mortality and 2D:4D, nor associations between 2D:4D and ACE1 allele or ACE2 genotype frequency. This absence of evidence is present for data taken from the second wave of COVID-19 in October 2020. Problematic theoretical grounding, individual-level conclusions drawn from national-level data, and issues with statistical inference in the original articles are discussed. Taken together, the current data offer no clear utility of 2D:4D in determining COVID-19 outcomes.

Conflicts in Bayesian Statistics Between Inference Based on Credible Intervals and Bayes Factors

In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside a credible interval but not supported by the Bayes factor (Type II conflict). Two computer programs in R have been developed that confirm the existence of a countable infinite number of cases, for which Bayes credible intervals are not compatible with Bayesian hypothesis testing.