Simula@BI - Bayesian hyperparameter learning
Simula@BI invites Professor in statistics Mattias Villani to give a talk on Bayesian statistical models.
Bayesian models typically involve both a high-dimensional set of parameters and a much smaller set of hyperparameters. The hyperparameters are used lower down the model hierarchy, further away from the data, and therefore more difficult to infer using traditional sampling-based methods.
In this talk, a Bayesian optimization method is presented for optimizing a marginal likelihood estimated by Monte Carlo simulation, e.g. MCMC. Professor Mattias Villani will also demonstrate the advantages of variational approximations of the posterior distribution for hyperparameter learning from the marginal likelihood or the commonly used log predictive score measure. The methods will be used to learn the hyperparameters in the steady-state vector autoregressive model and a time-varying parameter BVAR with stochastic volatility.