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

点击翻译按钮获取中文摘要

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.