TL;DR When implementing order-restrictions in JAGS, only the “ones trick” appears to yield the correct result. Consider two unknown chances, $\theta_1$ and $\theta_2$, that are assigned independent beta priors: $\theta_1 \sim \text{beta}(1,1)$ and $\theta_2 \sim \text{beta}(1,1)$. Let’s visualize the joint posterior by executing JAGS code (Plummer, 2003) and plotting the samples that are obtained from the MCMC algorithm. This is…

Recently we completed a multi-year Odyssey in order to obtain Bayes factors for partial correlations. The result is now available as a preprint. Instead of delving into the finer details of Bayes factors and posterior distributions, we will provide a concrete demonstration. Specifically, we will use Bayes factors for partial correlations to address a perennial question that has tormented children…

TL;DR We just preprinted a manuscript on how to teach the correlation coefficient with rectangles and squares. Check out the cool pictures. Suggestions for improvement are welcome. Abstract The equation for the Pearson correlation coefficient can be represented in a scatter plot as the difference in area between concordant and discordant rectangles, scaled by an area that represents the maximum possible…

In the previous post I discussed the problem of old evidence and wrote “It is highly likely that my argument is old, or even beside the point. I am not an expert on this particular problem.” Sure enough, Andrew Fowlie kindly attended me to the following book chapter by Roger Rosenkrantz: Rosenkrantz, R. D. (1983). Why Glymour is a Bayesian. In…

  To my shame and regret, I only recently found the opportunity to read the book “Bayesian philosophy of science” (BPS), by Jan Sprenger and Stephan Hartmann. It turned out to be a wonderful book, both in appearance, typesetting, and in contents. The book confirmed many of my prior beliefs ;- ) but it also made me think about the…

Recently I was asked to introduce Bayesian inference in three minutes flat. In 10 slides, available at https://osf.io/68y75/, I made the following points: Bayesian inference is “common sense expressed in numbers” (Laplace) We start with at least two rival accounts of the world, aka hypotheses. These hypotheses make predictions, the quality of which determines their change in plausibility: hypotheses that…

This month I gave a 45-minute presentation “Transparency in Science and Statistics” for the Italian Reproducibility Network. This presentation reflects my recent thinking on the topic. Important themes include “how to use a Ulysses contract to avoid fooling yourself (and others)”, “how to reveal uncertainty that often remains hidden”, “what is model-myopia (and how to avoid it)”, and “can Mertonian…

TLDR: ChatGPT rocks It has been more than two years since doing a post for the “Redefine Statistical Significance” series (https://www.bayesianspectacles.org/redefine-statistical-significance-xix-monkey-business/). In this series, Quentin Gronau and I demonstrated through countless examples that p-values just below .05 (“reject the null”!) should be interpreted with great caution, as such p-values provide –at best– only weak evidence against the null (see Benjamin…