不精确概率数值计算的随机最优化
Stochastic optimization for numerical evaluation of imprecise probabilities
摘要：
在不精确概率的应用中，分析师必须计算下（或上）期望，定义为一组参数值上期望的下确界。蒙特卡罗方法始终近似于固定参数值的期望值，但在网格搜索中实现以在参数空间的大子集上定位最小值可能是昂贵的。我们调查使用随机迭代寻根方法有效地计算较低的期望。在两个例子中，我们说明了使用各种随机逼近方法，并证明其优越的性能相比，网格搜索。
英文摘要：
In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed parameter values, but can be costly to implement in grid search to locate minima over large subsets of the parameter space. We investigate the use of stochastic iterative root-finding methods for efficiently computing lower expectations. In two examples we illustrate the use of various stochastic approximation methods, and demonstrate their superior performance in comparison to grid search.
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