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摘要翻译：
越来越明显的是，概率方法可以克服经典的最坏情况确定性框架的保守性和计算复杂性，并可能导致实际上更安全的设计。本文认为，全面的概率鲁棒性分析需要对鲁棒性函数进行详细的评估，并证明这种评估可以使用复杂度在不确定性空间维数上为线性的算法，以基本上任何期望的精度和置信度进行。此外，我们还表明，这类算法的平均内存需求是绝对有界的，完全在当今计算机的能力范围内。除了效率之外，我们的方法允许控制统计抽样误差和由于不确定度半径离散化引起的误差。对于特定的离散化误差容限水平，我们的技术提供了与精度水平成反比的传统方法的效率提高；也就是说，我们的算法随着精度要求的提高而变得更好。
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英文标题：
《Probabilistic Robustness Analysis -- Risks, Complexity and Algorithms》
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作者：
Xinjia Chen, Kemin Zhou and Jorge L. Aravena
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Applications 应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we argue that a comprehensive probabilistic robustness analysis requires a detailed evaluation of the robustness function and we show that such evaluation can be performed with essentially any desired accuracy and confidence using algorithms with complexity linear in the dimension of the uncertainty space. Moreover, we show that the average memory requirements of such algorithms are absolutely bounded and well within the capabilities of today's computers. In addition to efficiency, our approach permits control over statistical sampling error and the error due to discretization of the uncertainty radius. For a specific level of tolerance of the discretization error, our techniques provide an efficiency improvement upon conventional methods which is inversely proportional to the accuracy level; i.e., our algorithms get better as the demands for accuracy increase.
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PDF链接：
https://arxiv.org/pdf/707.0828
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