Mathematical Sciences: Saddlepoint Methods and Likelihood

鞍点法在 联合条件参数密度近似 功能协调发展的 预测推理的理论在很大程度上依赖于 这些近似似然的构造，这个理论 将在此奖项下继续发展。 但 鞍点法的一类潜在应用是 更广泛，这项研究的主要重点是 扩展到几个新的领域。 其中包括多变量 测试问题，其中可能性的零分布 比率统计量可以写成乘积Dirichlet形式，也 有限（不等概率）抽样方案和再抽样 非线性随机系统的响应分析 在工程学文献中很普遍。

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.