One-dimensional PDFs for all four planets under the assumption that the periods are in a 1:2:4:8 resonance. The periods are randomly sampled from 10,000 solutions for HR 8799e in the case where the orbits are non-crossing (Figure 9). The periods are then multipled by the appropriate factor for each planet. There is also generally a fairly fixed set of orbital parameters that fit this criteria for HR 8799b, with strong weighting toward specific values for T_o and ω. In addition, resonance is forced, and higher eccentricity solutions are preferred for HR 8799b and HR 8799d than we find in our other simulations.