Recent advances in data mining have integrated kernel functions with Bayesian probabilistic analysis of Gaussian distributions. These machine-learning approaches can incorporate prior information with new data to calculate probabilistic rather than deterministic values for unknown parameters. This article extensively analyzes a specific Bayesian kernel model that uses a kernel function to calculate a posterior beta distribution that is conjugate to the prior beta distribution. Numerical testing of the beta kernel model on several benchmark datasets reveals that this model's accuracy is comparable with those of the support vector machine (SVM), relevance vector machine, naive Bayes, and logistic regression, and the model runs more quickly than all the other algorithms except for logistic regression. When one class occurs much more frequently than the other class, the beta kernel model often outperforms other strategies to handle imbalanced datasets, including under-sampling, over-sampling, and the Synthetic Minority Over-Sampling Technique. If data arrive sequentially over time, the beta kernel model easily and quickly updates the probability distribution, and this model is more accurate than an incremental SVM algorithm for online learning.