Compared to mean regression and quantile regression, the literature on modal regression is very sparse. We propose a unified framework for Bayesian modal regression based on a family of unimodal distributions indexed by the mode along with other parameters that allow for flexible shapes and tail behaviors. Following prior elicitation, we carry out regression analysis of simulated data and datasets from several real-life applications. Besides drawing inference for covariate effects that are easy to interpret, we consider prediction and model selection under the proposed Bayesian modal regression framework. 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：与均值回归和分位数回归相比，关于众数回归的文献非常稀少。我们提出一个统一的贝叶斯众数回归框架，该框架基于一族以众数及其它参数为索引的单峰分布，这些参数允许灵活的形状和尾部行为。在完成先验设定后，我们对模拟数据以及多个实际应用场景中的数据集进行回归分析。除了对易于解释的协变量效应进行推断外，我们还考虑了所提出贝叶斯众数回归框架下的预测和模型选择。这些分析结果表明，所提出的推断过程对异常值具有极强的稳健性，使我们能够发现均值或中位数回归所忽略的有趣协变量效应，并能构建比均值或中位数回归更紧凑的预测区间。实现所提出贝叶斯众数回归的计算程序可在 https://github.com/rh8liuqy/Bayesian_modal_regression 获取。