Input values are a source of uncertainty for model predictions. When input uncertainty is characterized by a probability distribution, prediction uncertainty is characterized by the induced prediction distribution. Comparison of a model predictor based on a subset of model inputs to the full model predictor leads to a natural decomposition of the prediction variance and the correlation ratio as a measure of importance. Because the variance decomposition does not depend on assumptions about the form of the relation between inputs and output, the analysis can be called nonparametric. Variance components can be estimated through designed computer experiments.