论文标题
基于混合物分布的贝叶斯模态回归
Bayesian Modal Regression based on Mixture Distributions
论文作者
论文摘要
与平均回归和分位回归相比，关于模态回归的文献非常稀疏。基于该模式索引的单峰分布的家族以及允许灵活的形状和尾巴行为的其他参数，提出了贝叶斯模态回归的统一框架。在模式参数上不正确的先验下，后验礼仪的足够条件得出。事先启发后，对来自几个现实生活应用的模拟数据和数据集进行了回归分析。除了借鉴易于解释的协变量效应外，还考虑了提出的贝叶斯模态回归框架下的预测和模型选择。这些分析中的证据表明，所提出的推理程序对离群值非常强大，使人们能够发现比平均或中位回归中的有趣的均值或中位回归遗漏的有趣的协变量效应，并构建更严格的预测间隔。用于实施建议的贝叶斯模态回归的计算机程序可在https://github.com/rh8liuqy/bayesian_modal_regression上找到。
Compared to mean regression and quantile regression, the literature on modal regression is very sparse. A unifying framework for Bayesian modal regression is proposed, based on a family of unimodal distributions indexed by the mode, along with other parameters that allow for flexible shapes and tail behaviors. Sufficient conditions for posterior propriety under an improper prior on the mode parameter are derived. Following prior elicitation, regression analysis of simulated data and datasets from several real-life applications are conducted. Besides drawing inference for covariate effects that are easy to interpret, prediction and model selection under the proposed Bayesian modal regression framework are also considered. Evidence from these analyses suggest that the proposed inference procedures are very robust to outliers, enabling one to discover interesting covariate effects missed by mean or median regression, and to construct much tighter prediction intervals than those from mean or median regression. Computer programs for implementing the proposed Bayesian modal regression are available at https://github.com/rh8liuqy/Bayesian_modal_regression.
