I compare and contrast the two predominant philosophies for characterizing empirical uncertainty, frequentist and Bayesian statistics. The frequentist approach, in particular Neyman’s formulation of confidence intervals and Neyman-Pearson significance testing, held sway in much of the last century, but the Bayesian approach has experienced a dramatic revival in recent years. I’ll discuss why. While frequentist ideas remain essential for keeping our models from sending us off the rails, Bayes provides a comprehensive and logical inferential framework for addressing the entire spectrum of uncertainty, from extraterrestrial life to tennis strategy. The P-value debate, homeopathic treatments and ESP are discussed from the Bayesian and frequentist perspectives.