Runs and patterns with applications

拟议的研究计划是申请人目前关于游程和模式的分布理论及其在生物医学研究中的应用的研究的继续。总体而言，长期和短期目标都是为以运行和模式为基础的各种常用统计奠定理论基础，并将所开发的理论用于实际应用中的统计推断。拟议资助期的具体目标包括：(I)推导两个多态生物序列中最长公共子序列(LCS)长度的准确分布；(Ii)开发用于监测急诊室等待时间的游程模型；以及(Iii)扩展申请人先前在非重叠计数下多州试验中化合物模式的工作，以研究大样本的渐近性质。

The proposed research program is a continuation of the applicant's current research on the distribution theory of runs and patterns, and on its applications to biomedical research. In general, both long- and short-term objectives are to develop theoretical foundations for various commonly used statistics that are based on runs and patterns, and to use the developed theory for statistical inference in practical applications. The specific aims for the proposed funding period include: (i) deriving the exact distribution for the length of the longest common subsequence (LCS) among two multi-state biological sequences, (ii) developing a run-length model for monitoring emergency room (ER) waiting times, and (iii) extending the applicant's previous work on compound patterns in multi-state trials under non-overlap counting to study the asymptotic properties of large samples.