To complete the CTMC specification, we assume that all unnormalized rates in S are a priori independent and Gammadistributed with prior expectation m jk and variance d jk |v jk , following in the vein of Bayesian SSVS. However, little previous work on prior formulation helps inform our choices of m jk and v jk . This represents a critically important area of research. A common, yet arbitrary choice in the Bayesian phylogenetic literature assumes that rates draw from Exponential distributions, forcing m jk~vjk . We follow this practice in light of there being no obvious way to elicit information on the variance of these rates. Finally, we explore two choices for setting the means. The first assumes no preference over rates, setting all m jk~C , where C is an arbitrary constant; as, after normalization, only ratios of infinitesimal rates participate in the data likelihood, the actual value of C has no influence on the likelihood. The second is informed by the geographical distance between sites.