Computing ratios of normalizing constants plays an important role in statistical modeling. Two important examples are hypothesis testing in latent variables models, and model comparison in Bayesian statistics. In both examples, the likelihood ratio and the Bayes factor are defined as the ratio of the normalizing constants of posterior distributions. We propose in this article a novel methodology that estimates this ratio using stochastic approximation principle. Our estimator is consistent and asymptotically Gaussian. Its asymptotic variance is smaller than the one of the popular optimal bridge sampling estimator. Furthermore, it is much more robust to little overlap between the two unnormalized distributions considered. Thanks to its online definition, our procedure can be integrated in an estimation process in latent variables model, and therefore reduce the computational effort. The performances of the estimator are illustrated through a simulation study and compared to two other estimators : the ratio importance sampling and the optimal bridge sampling estimators.

翻译：计算归一化常数之比在统计建模中具有重要作用。两个重要示例包括潜变量模型中的假设检验，以及贝叶斯统计中的模型比较。在这两种情形中，似然比和贝叶斯因子均被定义为后验分布归一化常数之比。本文提出一种基于随机逼近原理估计该比值的新方法。所提估计量具有一致性与渐近正态性，其渐近方差小于常用的最优桥抽样估计量。更重要的是，该方法对两个未归一化分布间重叠度较低的情况具有更强的鲁棒性。得益于其在线计算特性，该流程可嵌入潜变量模型的估计过程中，从而显著降低计算成本。通过模拟研究展示了该估计量的性能，并与另外两种估计量（比率重要性抽样估计量与最优桥抽样估计量）进行了比较。