In the Bayesian linear regression modeling, we ran three chains from random initializations each with 10,000 samples, thinned to every 2 samples, and discarded the first 5000 samples from each as burn-in. We checked convergence by ensuring that R-hat, an estimate of the potential scale reduction of the posterior if sampling were to be infinitely continued, was below 1.1 (Gelman et al. 2014). The reported empirical 95% credible intervals (95% CI) represent the 2.5th to 97.5th percentiles of the highest posterior density interval calculated from the posterior samples.