Bayesian optimization of hyperparameters from noisy marginal likelihood estimates
提出一种新的贝叶斯优化框架，允许用户控制函数评估的计算精度，通过廉价噪声评估加速寻找最优超参数，应用于美国宏观经济时间序列数据的两个贝叶斯向量自回归模型。
Summary Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is an iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common situation in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo or importance sampling methods. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady‐state Bayesian vector autoregressive (BVAR) and the time‐varying parameter BVAR with stochastic volatility.