This isn't really correct on either point. A p-value is how a frequentist establishes "statistical significance," which is itself convoluted. It has really noth

This isn't really correct on either point. A p-value is how a frequentist establishes "statistical significance," which is itself convoluted. It has really nothing to do with validation. On the second point, frequentists very commonly split training and testing datasets, and so this practice is pretty much orthogonal to whether you're using Bayesian or frequentist methods.