Figure 1.

An illustration of how the second-stage model allows information to be shared among trials for condition k. The hyperparameters ${\{e_k^{(m)},f_k^{(m)}\}}_{m=1,2,\dots ,M}$ in the prior of ${\mathbf{\Lambda }}_k^{(i)}$ are estimated via empirical Bayes (described in Section 2.2) by pooling information from all trials. For the i-th trial, the Bayes’ rule then combines the evidence from single-trial data (likelihood) with the prior information to yield the posterior distribution of ${\mathbf{\Lambda }}_k^{(i)}(i=1,2,\dots ,N_k)$.