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We propose an easily computed estimator of marginal likelihoods fromposterior simulation output, via reciprocal importance sampling, combiningearlier proposals of DiCiccio et al (1997) and Robert and Wraith (2009). Thisinvolves only the unnormalized posterior densities from the sampled parametervalues, and does not involve additional simulations beyond the main posteriorsimulation, or additional complicated calculations. It is unbiased for thereciprocal of the marginal likelihood, consistent, has finite variance, and isasymptotically normal. It involves one user-specified control parameter, and wederive an optimal way of specifying this. We illustrate it with severalnumerical examples.

Easily Computed Marginal Likelihoods from Posterior Simulation Using the THAMES Estimator