Mathematical Sciences: Saddlepoint Methods and Likelihood

鞍点法在近似联合和条件参数密度函数方面特别有用。一种预测推理理论在很大程度上依赖于这些近似可能性的构造；这个理论将在这个奖项下继续发展。然而，鞍点方法的潜在应用范围要广泛得多，本研究的主要重点是将其扩展到几个新领域。这些问题包括多元检验问题，其中似然比统计的零分布可以写成乘积狄利克雷形式，也包括有限（不等概率）抽样方案和重抽样方案，以及工程文献中普遍存在的非线性随机系统的响应分析。

Saddlepoint methods have been particularly useful in the approximation of joint and conditional parametric density functions. A theory of predictive inference has drawn heavily on these constructions of approximate likelihoods; and this theory will continue to be developed under this award. However, the class of potential applications for saddlepoint methods is much broader, and the principal focus for this research is this expansion into several new areas. These include multivariate testing problems where the null distribution of the likelihood ratio statistics can be written in product Dirichlet form, also finite (unequal probability) sampling schemes and resampling schemes, and response analysis for non-linear stochastic systems prevalent in the engineering literature.