Abstract
Based on the observation that frequentist confidence intervals and Bayesian credible intervals sometimes happen to have the same numerical boundaries (under very specific conditions), Albers et al. (2018) proposed to adopt the heuristic according to which they can usually be treated as equivalent. We argue that this heuristic can be misleading by showing that it does not generalise well to more complex (realistic) situations and models. Instead of pragmatism, we advocate for the use of parsimony in deciding which statistics to report. In a word, we recommend that a researcher interested in the Bayesian interpretation simply reports credible intervals.
Highlights
Based on the observation that frequentist confidence intervals and Bayesian credible intervals sometimes happen to have the same numerical boundaries, Albers et al (2018) proposed to adopt the heuristic according to which they can usually be treated as equivalent
While we agree with their main observation, we disagree with their main conclusion
A simple regression example In Figure 1, we present some simulation results showing that Bayesian credible intervals do have the same properties as frequentist confidence intervals in the case of a simple regression model
Summary
Pragmatism should Not be a Substitute for Statistical Literacy, a Commentary on Albers, Kiers, and Van Ravenzwaaij (2018). Based on the observation that frequentist confidence intervals and Bayesian credible intervals sometimes happen to have the same numerical boundaries (under very specific conditions), Albers et al (2018) proposed to adopt the heuristic according to which they can usually be treated as equivalent. We argue that this heuristic can be misleading by showing that it does not generalise well to more complex (realistic) situations and models. We move to a discussion of two concrete examples examining the generalisability of the heuristic suggested by Albers et al (2018) in regards to the coverage properties (and the numerical boundaries) of confidence intervals and credible intervals
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