Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering method to estimate non-stationary trend of quantiles. We introduce general shrinkage priors to induce locally adaptive Bayesian inference on trends and mixture representation of the asymmetric Laplace likelihood. To quickly compute the posterior distribution, we develop calibrated mean-field variational approximations to guarantee that the frequentist coverage of credible intervals obtained from the approximated posterior is a specified nominal level. Simulation and empirical studies show that the proposed algorithm is computationally much more efficient than the Gibbs sampler and tends to provide stable inference results, especially for high/low quantiles.

翻译：分位数是随机变量的重要特征，相较于均值等常用汇总统计量，能提供关于分布的更丰富信息。本文提出一种贝叶斯分位数趋势滤波方法，用于估计分位数的非平稳趋势。我们引入广义收缩先验以对趋势进行局部自适应贝叶斯推断，并采用非对称拉普拉斯似然的混合表示。为快速计算后验分布，我们开发了校准平均场变分逼近方法，以确保近似后验所得的置信区间在频率学派框架下的覆盖率达到指定的名义水平。模拟与实证研究表明，所提算法在计算效率上显著优于吉布斯采样器，尤其在极端高分位数与低分位数情形下，能提供更稳定的推断结果。