Research in Nuclear Applications of Statistics, Population Genetics, and Probability Bounds

该建议描述了一类行为是随机的，需要概率和统计工具进行分析的科学问题。一个重要的类是关于CANDU反应堆的建模和核安全。最初的安全裕度是基于反应堆设计的确定性或极限包络计算。 在多年的运行中，存在堆芯老化效应，例如压力管的辐照和流动引起的腐蚀，这需要统计方法来确定反应堆在当前条件下是否满足运行许可证，即它们是否需要在降低的功率下运行，从而导致收入损失。该提案的一部分涉及开发所需的统计工具，并涉及大学与核工业的合作。申请人之前的一项重要贡献涉及皮克林核电站A的进料管，其中严格的统计方法使工业受益，他表明不需要额外的大量采样，从而缩短了反应堆单元需要停机的时间。 这项工作已包括在向加拿大核安全委员会成功提交的重新启动函中。未来的研究方向包括中子过功率保护和通道/束功率合规性的最佳估计和不确定性分析。统计方法的好处是，在遵守必要的安全标准的同时，为许可证限制提供更好的裕度。 另一个领域涉及种群遗传学和生态学中的分区分布。这些分布描述了观察到的群体变化。对这些分布的理解揭示了可以从观测数据中推断出的潜在进化过程。 申请人已经开发了一个框架，其中许多这些分区可以从一个统一的原则推导出来，他希望使用这种方法来开发工具，用于推断导致观察到的物种多样性和遗传变异的进化力量。 最后一类问题是关于开发和扩展的方法，最近发现的有限的信息，如第一次和第二次的时刻，通过铸造这些界限更普遍的期望的整数值随机变量的界限，获得一般的多元概率界限。

This proposal describes classes of scientific problems whose behaviour is stochastic and which require probabilistic and statistical tools for their analyses. One important class is concerned with modeling and nuclear safety in CANDU reactors. The original safety margins were based on deterministic or limit of envelope calculations based on reactor design. Over years of operation there are core aging effects such as irradiation of pressure tubes and flow induced corrosion which necessitates statistical methods to determine whether reactors meet operating licenses under current conditions of whether they need to operate at reduced power with consequent loss of revenue. Part of this proposal is concerned with developing needed statistical tools and involves university collaboration with the nuclear industry. A significant previous contribution by the applicant in which a rigorous statistical approach benefited the industry concerned the feeder pipes at Pickering Nuclear Generating Station A where he showed that additional large sampling was unnecessary, thus shortening the time the reactor units were required to be down. This work was included in the successful submission of restart letters to the Canadian Nuclear Safety Commission. Potential future directions of research include best estimate and uncertainty analysis to neutron overpower protection and channel/bundle power compliance. A statistical approach provides benefits in providing better margins to the license limits while adhering to necessary safety standards. Another area concerns partition distributions in population genetics and ecology. These distributions describe the observed variation in populations. An understanding of these distributions sheds light on the underlying evolutionary processes that can be inferred from observed data. The applicant has developed a framework in which many of these partitions can be derived from one unifying principle and he hopes to use this approach to develop tools for making inferences about the evolutionary forces which have led to the observed diversity of species and genetic variation. The last class of problems is concerned with developing and extending a methodology recently discovered for obtaining general multivariate probability bounds with limited information, such as first and second moments, by casting these bounds more generally as bounds on the expectation of an integer-valued random variable.