Hyperparameters: Optimize, or Integrate Out?

摘要: I examine two approximate methods for computational implementation of Bayesian hierarchical models, that is, models which include unknown hyperparameters such as regularization constants. In the ‘evidence framework’ model parameters are integrated over, and resulting evidence is maximized over hyperparameters. The optimized used to define a Gaussian approximation posterior distribution. alternative ‘MAP’ method, true probability found by integrating then parameters, made. similarities approaches, their relative merits, discussed, comparisons made with ideal solution.