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…