Bayesian inference for the correlation in the presence of estimation uncertainty. The gray points show the point estimates and plotted against their true values (Step 1). The black points show the posterior means of the inferred µT1 and µT2 parameters from the hierarchical analysis plotted against their true values (Step 2). The horizontal black arrows indicate the range of the true values; the vertical gray and black arrows indicate the ranges of the point estimates and the inferred parameters, respectively. The inferred parameters are less dispersed than the point estimates. The bottom panel shows the posterior distribution of the correlation ρ from the hierarchical analysis: it more closely approximates the true correlation (dashed line) between µT1 and µT2 than the Pearson correlation coefficient r computed between the point estimates (dotted line).