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：与平均回归和四分位回归相比,关于模式回归的文献非常稀少。 我们提出一个统一的巴伊西亚模式回归框架,其依据是按模式索引的单式分布式组合,以及允许灵活形状和尾部行为的其他参数。在事先引出后,我们对若干实际应用的模拟数据和数据集进行回归分析。除了对易于解释的共变效应进行推论外,我们还考虑根据拟议的巴伊西亚模式回归框架进行预测和模型选择。这些分析的证据表明,拟议的推论程序对外端非常有力,使人们能够发现中度或中位回归所遗漏的有趣的共变效应,并比中度回归的预测间隔更严格得多。 实施拟议的巴伊斯模式回归的计算机程序可在https://github.com/rh8liuqy/Bayesian_modal_regresion上查阅。