AbstractThe Lowest Radial Distance (LoRaD) method is a modification of the recently introduced Partition-Weighted Kernel method for estimating the marginal likelihood of a model, a quantity important for Bayesian model selection. For analyses involving a fixed tree topology, LoRaD improves upon the Steppingstone or Thermodynamic Integration (Path Sampling) approaches now in common use in phylogenetics because it requires sampling only from the posterior distribution, avoiding the need to sample from a series of ad hoc power posterior distributions, and yet is more accurate than other fast methods such as the Generalized Harmonic Mean (GHM) method. We show that the method performs well in comparison to the Generalized Steppingstone method on an empirical fixed-topology example from molecular phylogenetics involving 180 parameters. The LoRaD method can also be used to obtain the marginal likelihood in the variable-topology case if at least one tree topology occurs with sufficient frequency in the posterior sample to allow accurate estimation of the marginal likelihood conditional on that topology. [Bayesian; marginal likelihood; phylogenetics.]