We propose an easily computed estimator of marginal likelihoods from posterior simulation output, via reciprocal importance sampling, combining earlier proposals of DiCiccio et al (1997) and Robert and Wraith (2009). This involves only the unnormalized posterior densities from the sampled parameter values, and does not involve additional simulations beyond the main posterior simulation, or additional complicated calculations. It is unbiased for the reciprocal of the marginal likelihood, consistent, has finite variance, and is asymptotically normal. It involves one user-specified control parameter, and we derive an optimal way of specifying this. We illustrate it with several numerical examples.

翻译：我们提出一种通过倒数重要采样从后验模拟输出中易计算的边缘似然估计量，该估计量结合了DiCiccio等(1997)和Robert与Wraith(2009)的早期建议。该方法仅需利用采样参数值处的非归一化后验密度，无需在主后验模拟之外进行额外模拟或执行复杂计算。该估计量对边缘似然倒数具有无偏性、一致性、有限方差且渐近正态性。它涉及一个用户指定的控制参数，我们推导出其最优取值方式。通过多个数值算例对该方法进行验证。