Statistical descriptions of reaction times are central components of quantitative attention models. It is often assumed that total reaction time is comprised of various components, e.g. sensory delays, decision making and motor execution contributions. We use machine learning to decompose observed total reaction times into sensorimotor and decision components, and evaluate which model assumptions maximize approximate Bayesian model evidence (free energy or evidence lower bound). We find that an inverse Gaussian decision time distribution combined with a very narrow Gaussian sensorimotor distribution can best explain human reaction time data. We also model outliers explicitly by a uniform background distribution. We find that the model assigns a small fraction of datapoints to this outlier distribution