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.

翻译：相较于均值回归与分位数回归，现有关于众数回归的文献十分有限。本文提出了一种基于单峰分布族的贝叶斯众数回归统一框架，该分布族以众数为索引参数，并包含其他允许灵活形态与尾部行为的参数。我们推导了在众数参数采用非信息先验时后验分布适定性的充分条件。通过先验设定，对模拟数据及多个实际应用数据集进行了回归分析。除可解释协变量效应的推断外，本研究还探讨了所提贝叶斯众数回归框架下的预测与模型选择问题。分析结果表明，所提出的推断程序对异常值具有极强的稳健性，能够发现均值或中位数回归所忽略的显著协变量效应，并能构建比均值或中位数回归更紧凑的预测区间。实现该贝叶斯众数回归的计算机程序可在 https://github.com/rh8liuqy/Bayesian_modal_regression 获取。