Bayesian model comparison implements Occam's razor through its sensitivity to the prior. However, prior-dependence makes it important to assess the influence of plausible alternative priors. Such prior sensitivity analyses for the Bayesian evidence are expensive, either requiring repeated, costly model re-fits or specialised sampling schemes. By exploiting the learned harmonic mean estimator (LHME) for evidence calculation we decouple sampling and evidence calculation, allowing resampled posterior draws to be used directly to calculate the evidence without further likelihood evaluations. This provides an alternative approach to prior sensitivity analysis for Bayesian model comparison that dramatically alleviates the computational cost and is agnostic to the method used to generate posterior samples. We validate our method on toy problems and a cosmological case study, reproducing estimates obtained by full Markov chain Monte Carlo (MCMC) sampling and nested sampling re-fits. For the cosmological example considered our approach achieves up to $6000\times$ lower computational cost.

翻译：贝叶斯模型比较通过其对先验的敏感性实现了奥卡姆剃刀原则。然而，这种先验依赖性使得评估合理替代先验的影响至关重要。针对贝叶斯证据的此类先验敏感性分析计算成本高昂，通常需要重复且代价巨大的模型重新拟合或专门的采样方案。通过利用学习调和平均估计器（LHME）进行证据计算，我们将采样与证据计算解耦，使得重采样的后验样本可直接用于计算证据，无需额外的似然函数评估。这为贝叶斯模型比较的先验敏感性分析提供了一种替代方法，显著降低了计算成本，并且与生成后验样本的具体方法无关。我们在玩具问题和宇宙学案例研究上验证了该方法，重现了通过完整马尔可夫链蒙特卡洛（MCMC）采样和嵌套采样重新拟合获得的估计结果。在所考虑的宇宙学示例中，我们的方法实现了高达$6000\times$的计算成本降低。