论文标题
使用校准的变异近似值快速和局部自适应贝叶斯分位数平滑
Fast and Locally Adaptive Bayesian Quantile Smoothing using Calibrated Variational Approximations
论文作者
论文摘要
分位数是随机变量的有用特征，与常用的摘要统计数据（例如均值）相比，可以提供有关分布的大量信息。在本文中，我们提出了一种贝叶斯分位趋势滤波方法来估计分位数的非平稳趋势。我们介绍了一般的收缩先验，以诱导局部适应性的贝叶斯对趋势和混合物表示不对称的拉普拉斯可能性的表述。为了快速计算后验分布，我们开发出校准的平均场变异近似值，以确保从近似后验获得的可信间隔的频繁覆盖范围是指定的标称水平。模拟和实证研究表明，所提出的算法在计算上比Gibbs采样器要高得多，并且倾向于提供稳定的推理结果，尤其是对于高/低分位数。
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.
