Monte Carlo Analysis: A New Paradigm not Requiring Apriori Probability Distributions

ECS-9811051 Barmish这是一个建立一个为期三年的研究项目的建议。这个建议的动机是来自最近的结果，在新出现的领域的概率鲁棒性。人们认为，一个成功的项目将有依赖于蒙特卡罗模拟的许多领域的影响，区别于现有文献的关键点，本研究建议如下：不同于经典的蒙特卡罗模拟，新的方法正在考虑几乎不需要先验信息的概率分布的不确定参数。在这个新的框架中，给定的数据与具有真实的参数不确定性的经典鲁棒性理论中的数据完全相同;即，仅假设数学输入-输出模型和每个不确定参数的上界和下界。这就提出了以下问题：在蒙特卡罗环境中使用什么样的概率分布是有意义的？当没有可用的概率分布时，是否有一种有意义的方法来“编程”蒙特卡罗模拟的随机数发生器？在该提案的主体，这些问题进行了更详细的审查，并提出了研究的目的是在其resolution.Preliminary结果激励拟议的研究表明，抽样的不确定性，往往应该进行的方式，这是完全不同的从经典的蒙特卡罗计划。例如，在正文中，描述了涉及两级放大器的案例研究。抽样分布原来需要截断的概率分布的两个不确定的电容器。这样的分布不是通常用于蒙特卡罗电路分析的分布。最终的结果是，使用传统的蒙特卡罗方案的“成功操作的概率”的预测受到挑战。研究的主要目标之一是展示新思想在许多应用领域的适用性，并将“老式蒙特卡洛”结果与使用新方法获得的结果进行比较。有人认为，经典的蒙特卡罗分析往往导致预测是过于乐观的。这种情况（可用的边界，但没有统计）是相当典型的系统科学领域时，一个方法的鲁棒性的背景下，或通过区间分析方法的问题。总之，所提出的研究集中在一个可靠的概率分布是不可用的问题。鉴于蒙特卡罗理论假设一个分布作为理论的输入，所提出的工作涉及找到“适当的”分布作为理论的输出;即，该理论首先确定适当的分布，然后才进行计算机模拟。2拟议研究的出发点是一种描述不确定性的新型范式-由首席研究员与他的研究生合作开发。与上面的例子一致，这个新的范例只需要随机变量的百分比误差的先验界。唯一需要的另一个假设是，与平均值的大偏差比小偏差的可能性小。 ***

ECS-9811051BarmishThis is a proposal to set up a three year research project. The motivation for this proposal is derived from the recent results in the newly emergent area of Probabilistic Robustness. It is felt that a successful project would have an impact on many fields which rely on Monte Carlo simulation, The critical point distinguishing this proposed research from existing literature is as follows: Unlike classical Monte Carlo simulation, the new approach being considered requires almost no apriori information about the probability distribution for the uncertain parameters. In this new framework, the given data is exactly the same as in classical robustness theory with real parametric uncertainty; i.e., only a mathematical input-output model and upper and lower bounds for each uncertain parameter are assumed. This raises the following questions: What probability distribution makes sense to use in a Monte Carlo context? Is there a meaning way to 'prograrn" the random number generator for Monte Carlo simulation when no probability distribution is available? In the body of the proposal, these questions are examined in greater detail and the proposed research aimed at their resolution.Preliminary results motivating the proposed research suggest that sampling of uncertainty should often be carried out in a way which is quite different from classical Monte Carlo schemes. For example, in the body, a case study involving a 2-stage amplifier is described. The sampling distribution turns out to require truncation of the probability distribution for the two uncertain capacitors. Such a distribution is not one which would normally be used in a Monte Carlo circuit analysis. The end result is that a prediction of the 'probability of successful operation" using a traditional Monte Carlo scheme is subjected to challenge. One of the main objectives of the research is to demonstrate applicability of the new ideas to many application areas and compare 'old style Monte Carlo" results with the results obtained using the new approach. It is felt that classical Monte Carlo analysis often leads to predictions which are unduly optimistic.This situation (the availability of bounds but no statistics) is quite typical in the Systems Science area when one approaches a problem in a robustness context or via interval analysis methods. In summary, the proposed research concentrates on problems for which a reliable probability distribution is unavailable. Whereas Monte Carlo theory assumes a distribution as input to the theory, the proposed work involves finding the 'appropriate" distribution as the output of the theory; i.e., the theory first determines the appropriate distribution, and, only then is computer simulation carried out.The starting point for the proposed research is a new type of paradigm to describe uncertainty - developed by the Principal Investigator in collaboration with his graduate student. Consistent with the example above, this new paradigm requires only apriori bounds on the percentage errors for the random variables. The only other assumption required is that large deviations from the mean are less probable than small deviations. ***