We are in the era of abundant big or high-dimensional data. These data afford us the opportunity to discover predictors of an event of interest, and to estimate occurrence of the event based on values of these predictors. For example, genome-wide association studies examine millions of single-nucleotide polymorphisms (SNPs), along with disease status. We can learn SNPs that affect disease status from these data sets, and use the knowledge learned to predict disease likelihood. Owing to the large number of features, it is difficult for many prediction methods to use all the features directly. The ReliefF algorithm ranks a set of features in terms of how well they predict a target. It can be used to identify good predictors, which can then be provided to a prediction method. We compared the performance of eight prediction methods when predicting binary outcomes using high-dimensional discrete data sets. We performed two-stage prediction, where ReliefF is used in the first stage to identify good predictors. Bayesian network (BN)-based methods performed best overall. Furthermore, ReliefF did not improve their performance. The BN-based methods use the Bayesian Dirichlet Equivalent Uniform score to evaluate candidate models, and use BN inference algorithms to perform prediction. This score and these algorithms were developed for discrete variables. This perhaps explains why they perform better in this domain. Many prediction methods are available, and researchers have little reason for choosing one over the other in the domain of binary prediction using high-dimensional data sets. Our results indicate that the best choices overall are BN-based methods. 