Prior sensitivity analysis is a fundamental method to check the effects of prior distributions on the posterior distribution in Bayesian inference. Exploring the posteriors under several alternative priors can be computationally intensive, particularly for complex latent variable models. To address this issue, we propose a novel method for quantifying the prior sensitivity that does not require model re-fit. Specifically, we present a method to compute the Hellinger and Kullback-Leibler distances between two posterior distributions with base and alternative priors, as well as posterior expectations under the alternative prior, using Monte Carlo integration based only on the base posterior distribution. This method significantly reduces computational costs in prior sensitivity analysis. We also extend the above approach for assessing the influence of hyperpriors in general latent variable models. We demonstrate the proposed method through examples of a simple normal distribution model, hierarchical binomial-beta model, and Gaussian process regression model.

翻译：先验敏感性分析是贝叶斯推断中检验先验分布对后验分布影响的基本方法。在多种替代先验下探索后验分布可能计算量巨大，尤其对于复杂潜变量模型。为解决此问题，我们提出一种无需模型重拟合即可量化先验敏感性的新方法。具体而言，我们提出基于基础后验分布进行蒙特卡洛积分的方法，用于计算基础先验与替代先验下两个后验分布间的Hellinger距离与Kullback-Leibler散度，以及替代先验下的后验期望。该方法显著降低了先验敏感性分析的计算成本。我们还将上述方法扩展至评估一般潜变量模型中超先验的影响。通过简单正态分布模型、分层二项-贝塔模型及高斯过程回归模型的示例，我们验证了所提方法的有效性。