Mathematical Sciences: Models and Methodology for Positive Dependence

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Within the framework of positive dependence and reliability theory, a number of major research topics in statistics and applied probability modeling are proposed. These include: (a) development of the statistical applications of metrics and related orderings on permutations; (b) new and more efficient isotonic regression algorithms for partially ordered spaces; and (c) various techniques for types of ordinal data analyses. Additional topics include reliability maintenance models, models and methodology for random length multivariate normal data, and combinatoric identities arising from nonhomogeneous Poisson processes. The research approaches to these topics employ results and techniques from positive dependence, reliability theory and multivariate analysis. The principal investigators will explore a number of theoretical topics in the area of multivariate statistical analysis called positive dependence and consider a number of applications of these theoretical results. In particular the investigators plan to develop new computational algorithms that are more efficient than current algorithms. The purpose of this research is to develop strategies for maintaining a system in an optimal fashion balancing the cost of maintenance against the cost of break-downs.