An automated prior robustness analysis in Bayesian model comparison
针对贝叶斯模型比较中边际似然对先验超参数敏感但鲜少检验的问题，提出在MCMC估计中自动计算边际似然对任意先验超参数敏感性的高效方法，并用多元时间序列模型实例验证。
Summary It is well‐known that the marginal likelihood, the gold standard for Bayesian model comparison, can be sensitive to prior hyperparameter choices. However, most models require computationally intense simulation‐based methods to evaluate the typically high‐dimensional integral of the marginal likelihood expression. Hence, despite the recognition that prior sensitivity analysis is important in this context, it is rarely done in practice. We develop efficient and feasible methods to compute the sensitivities of the marginal likelihood, obtained via two common simulation‐based methods, with respect to any prior hyperparameter, alongside the Markov chain Monte Carlo (MCMC) estimation algorithm. Our approach builds on automatic differentiation (AD), which has only recently been introduced to the more computationally intensive MCMC simulation setting. We illustrate our approach with two empirical applications in the context of widely used multivariate time series models.