Bayesian Mode Regression

Abstract

Like mean, quantile and variance, mode is also an important measure of central tendency of a distribution. Many practical questions, particularly in the analysis of big data, such as \Which element (gene or le or signal) is the most typical one among all elements in a network?" are directly related to mode. Mode regression, which provides a convenient summary of how the regressors a ect the conditional mode, is totally di erent from other models based on conditional mean or conditional quantile or conditional variance. Some inference methods for mode regression exist but none of them is from the Bayesian perspective. This paper introduces Bayesian mode regression by exploring three different approaches, including their theoretic properties. The proposed approacher are illustrated using simulated datasets and a real data set.