A linear analysis of thermal instabilities along the magnetic field lines in the plasma edge is used to derive predictive algorithms for the edge density limit for the onset of multifaceted asymmetric radiation from the edge (MARFE) within the last closed flux surface in tokamaks. Calculated MARFE onset density limits for representative impurity and recycling neutral concentrations and representative edge plasma parameters in a model problem exhibit the expected strong dependence on impurity type and concentration at low recycling neutral concentrations. At recycling neutral concentrations greater than ~1 × 10-5, the MARFE onset density limit is found to depend strongly on the recycling neutral concentration and to be relatively independent of impurity type or concentration. Predicted MARFE onset density limits for two DIII-D shots agree reasonably well with experimental data.