Bayesian optimization of hyperparameters from noisy marginal likelihood estimates

Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. optimization is an iterative method where Gaussian process posterior underlying function sequentially updated new evaluations. We propose novel framework for situations user controls computational effort and therefore precision This common in econometrics likelihood computed Markov chain Monte Carlo or importance sampling methods. The acquisition strategy gives optimizer option to explore with cheap noisy evaluations find optimum faster. applied estimating prior two popular on US macroeconomic time series data: steady-state vector autoregressive (BVAR) time-varying parameter BVAR stochastic volatility.