Studies in branching, population genetics, probability bounds, and prediction in nuclear safety analysis

该建议描述了其行为在本质上是随机的，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。 随着这些反应堆的老化，安全裕度降低，有必要采用统计方法来确定它们是否符合当前条件下的运营许可证，是否需要降低额定值。 降低反应堆的额定值意味着它必须在降低的功率下运行，同时损失巨大的收入。 以前，进行确定性安全分析或考虑极端操作条件的包络线计算极限就足够了。 这种方法不太现实，需要用统计方法取代。该提案将继续与安大略发电公司的科学家和工程师合作。 申请人以前最重要的贡献之一涉及皮克林核发电站A的馈线管道，其中严格的统计方法使该行业受益，他表明没有必要进行额外的大规模取样，从而缩短了向加拿大核安全委员会提交重启函的时间和在反应堆机组停机时损失的收入。 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。统计方法的好处在于，在遵守安全标准的同时，为许可证限制提供更好的裕度。 另一类问题涉及群体遗传学和生态学中的分区分布。 这些分布描述了当今人口中观察到的变化。 了解这些分布有助于了解潜在的进化过程。 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，并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。

This proposal describes scientific problems whose behaviour is stochastic in nature and which require probabilistic and statistical tools for their analysis. One important class is concerned with modeling and nuclear safety in CANDU reactors. As these reactors age, safety margins decrease and it becomes necessary to adopt statistical methods to determine whether they meet operating licenses under current conditions of whether they need to be de-rated. De-rating a reactor means it must operated at reduced power with an enormous loss of revenue. Previously, it was adequate to carry out deterministic safety analyses or limit of envelope computations that took into account extreme operating conditions. Such methods are unduly unrealistic and need to be replaced with statistical methods. This proposal continues collaboration with scientists and engineers at Ontario Power Generation. One of the most significant previous contributions by the applicant in which a rigorous statistical approach benefited the industry involved the feeder pipes at Pickering Nuclear Generating Station A where he showed that additional large sampling was unnecessary, thus shortening the time and lost revenue while the reactor units were down, for 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 safety standards. Another class of problems concerns partition distributions in population genetics and ecology. These distributions describe the observed variation in present day population. Understanding these distributions sheds light on the underlying evolutionary process. The applicant has developed a framework in which many of these partitions can be derived from one unifying principle and 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.