This paper compares the predictive performance and efficiency of several machine-learning methods when applied to a genome-wide dataset on Alzheimer's disease that contains 312,318 SNP measurements on 1411 cases. In particular, a Bayesian algorithm is introduced and compared to several standard machine-learning methods. The results show that the Bayesian algorithm predicts outcomes comparably to the standard methods, and it requires less total training time. These results support the further development and evaluation of the Bayesian algorithm.