Abstract In this article, two Bayesian kernel methods, namely the Gaussian process regression (GPR) and relevance vector machine (RVM) techniques, are used to estimate illumination chromaticity and predict the reliability of the estimation process, which is not accessible for most machine learning techniques that have been used for color constancy. More than seven kinds of GPR covariance function and their combinations, and an RVM method using Gaussian, Laplace and Cauchy kernel functions, have been used on two real image sets. The experimental results show that the GPR method outperforms those based on RVM and ridge regression using stationary covariance functions, and GPR can almost achieve the same performance as support vector regression (SVR). The performance of the RVM for regression is almost the same as that of GPR using the dot product covariance function. The influence of outliers on the data with Gaussian noise is analyzed in detail via using heavy-tailed Laplace and Student-t kernel functions when GPR and the RVM are used for color constancy.