Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is a popular iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. An acquisition strategy uses this posterior distribution to decide where to place the next function evaluation. 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 (MCMC) or importance sampling methods, with the precision of the marginal likelihood estimator determined by the number of samples. 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. The proposed method is shown to find the optimum much quicker than traditional Bayesian optimization or grid search.
翻译:Bayesian优化是一种流行的迭代方法,其基础功能的高斯进程后半导体通过新的功能评价按顺序更新。一种购置战略使用这种后部分布来决定下一个函数评价的位置。我们为用户控制计算努力从而控制功能评价的精确度的情况提出了一个新的Bayesian优化框架。这是一种常见的生态计量方法,其边际可能性常常由Markov链 Monte Carlo(MCMC)或重要性取样方法计算,其精密性是样品数量决定的边际概率估测器。新的购置战略使优化者能够以廉价的噪音评价来探索功能,从而找到最佳的更快。该方法用于估算美国宏观经济时间序列数据中两种流行模型中的先前超比对准度:稳定状态的Bayesian矢量自动递增(BVAR)和时间变换参数BVAR(BVAR)的不稳定性取样方法,其精准度由样品数量决定。新的购置战略使优化者能够以廉价的噪音评价方式探索功能,从而找到最佳的速度更快地利用美国宏观经济时间序列数据中的两个模型:稳定的BVAR自动递增速度。