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：量子是随机变量的有用特征,这些变量能够提供与常用的简要统计(例如手段)相比关于分布的大量信息。在本文中,我们建议采用贝叶斯四分位趋势过滤法来估计四分位数的非静止趋势。我们采用了一般缩微前科,以诱使贝叶斯人对不对称拉皮尔可能性的趋势和混合表示进行本地适应性推断。为了快速计算后方分布,我们开发了经校准的平均场变差近似值,以确保从近似后端获得的可靠间隔的频繁覆盖是一个特定的名义水平。模拟和实证研究表明,拟议的算法比吉布斯取样员在计算上效率要高得多,而且往往提供稳定的推论结果,特别是高/低位四分位数。