Estimating Posterior Sensitivities with Application to Structural Analysis of Bayesian Vector Autoregressions
扩展了经典模拟中的无穷小扰动分析，通过吉布斯采样计算后验统计量对先验参数的渐近无偏一致敏感性，并在美国宏观经济时间序列的贝叶斯向量自回归中展示了其对脉冲响应和方差分解等关键结果的影响。
The inherent feature of Bayesian empirical analysis is the dependence of posterior inference on prior parameters, which researchers typically specify. However, quantifying the magnitude of this dependence remains difficult. This article extends Infinitesimal Perturbation Analysis, widely used in classical simulation, to compute asymptotically unbiased and consistent sensitivities of posterior statistics with respect to prior parameters from Markov chain Monte Carlo inference via Gibbs sampling. The method demonstrates the possibility of efficiently computing the complete set of prior sensitivities for a wide range of posterior statistics, alongside the estimation algorithm using Automatic Differentiation. The method’s application is exemplified in Bayesian Vector Autoregression analysis of fiscal policy in U.S. macroeconomic time series data. The analysis assesses the sensitivities of posterior estimates, including the Impulse response functions and Forecast error variance decompositions, to prior parameters under common Minnesota shrinkage priors. The findings illuminate the significant and intricate influence of prior specification on the posterior distribution. This effect is particularly notable in crucial posterior statistics, such as the substantial absolute eigenvalue of the companion matrix, ultimately shaping the structural analysis.