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

这一建议描述了行为是随机的、需要概率和统计工具进行分析的各类科学问题。一个重要的课程是关于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包络极限计算。在多年的运行中，存在压力管辐照和流动诱导腐蚀等堆芯老化效应，这就需要统计方法来确定反应堆在当前条件下是否符合运营许可证，即它们是否需要在降低功率的情况下运行，从而造成收入损失。该提案的一部分涉及开发必要的统计工具，并涉及大学与核工业的合作。申请人以前的一项重大贡献是采用严格的统计方法，使工业受益，涉及皮克林核电站A的馈线管道，他在那里表明，不需要额外的大样本，从而缩短了反应堆机组需要停机的时间。这项工作包括在成功地向加拿大核安全委员会提交的重启信函中。未来可能的研究方向包括对中子过功率保护和通道/束流功率顺应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利润率。另一个领域涉及种群遗传学和生态学的分区分布。这些分布描述了观察到的种群变异。对这些分布的理解有助于揭示从观测数据中可以推断出的潜在进化过程。申请人已经开发了一个框架，其中许多这样的划分可以从一个统一的原则中得到，他希望使用这种方法来开发工具来推断导致观察到的物种多样性和遗传变异的进化力量。最后一类问题涉及开发和扩展最近发现的方法，通过将这些界更一般地作为整数值随机变量的期望的界，在有限信息(如一阶和二阶矩)下获得一般的多变量概率界。

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.