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.

翻译：在应用不精确的概率方面,分析师必须计算较低的(或更高的)预期值,即对一组参数值的预期最小值。蒙特卡洛方法始终以固定参数值为大致预期值,但在网格搜索中,为了在参数空间的大型子集上找到迷你,实施这种方法成本很高。我们调查使用随机迭代根调查方法来高效计算较低期望值。在两个例子中,我们举例说明了各种随机近似方法的使用情况,并展示了这些方法与网格搜索相比的优异性能。