Algorithms, Approximations, and Valid Statistical Inference

9971586通过使用算法和精确的近似值，已经找到了解决困难统计问题的新方法。 有时，这些解决方案可能极难实现，而且解决方案的统计属性以及由此产生的统计推断可能很难描述，在最坏的情况下，甚至无效。 拟议研究的总主题是为各种问题开发计算算法，精确近似和其他数值技术，并以有效的统计推断结果的方式进行。 一些具体的项目是发展分层和缺失数据模型的算法，包括扩展EM算法估计方程;使用精确的近似和贝叶斯和频率论方法的综合，以提供在滋扰参数问题的有效推断;以及离散数据问题中的计算和推理，特别注意鞍点近似的数值替代方法和蒙特卡罗方法的新用途。当前统计学的许多研究受到异常快速计算的影响，这导致了对解决许多问题的方法的重新审查。 这些新方法为以前未解决的问题提供了一些解决方案;然而，它们的实现通常并不简单，因此解决方案仅适用于少数专家用户。 这种情况出现在流行病学研究中，以估计临床乳腺炎的影响，其中目前可用的算法的实施并不清楚。 在这种情况下，以及在其他应用中，例如估计癌症集群相对于有毒废物场地的位置，这里提出的解决方案类型是直接实施的。 这种新的解决方案还将导致统计上有效的结论，计算密集型程序并不总是具有这种特性。 除了这些算法，新的统计模拟方法的研究提出了在遗传学和生物技术研究（染色体上的位置的链接到特定的疾病）中的应用。

9971586New solutions to difficult statistical problems have been found through the use of algorithms and accurate approximations. Sometimes these solutions can be extremely difficult to implement and, moreover, the statistical properties of the solution, and hence the resulting statistical inference, may be difficult to describe and, in the worst cases, even invalid. The general theme of the proposed research is to develop computing algorithms, accurate approximations, and other numerical techniques for a variety of problems, and do it in such a way that a valid statistical inference results. Some specific projects are the development of algorithms for hierarchical and missing data models, including extensions of the EM algorithm to estimating equations; using accurate approximations and a synthesis of Bayesian and frequentist approaches to provide valid inferences in nuisance parameter problems; and computation and inference in discrete data problems, with particular attention to numerical alternatives to saddlepoint approximations and novel uses of Monte Carlo methods.Much current research in statistics is influenced by the availability of exceptionally fast computing, which has led to a reexamination of the approaches to many problems. These new approaches have provided some solutions to previously unsolved problems; however, their implementation is often not straightforward so the solutions will not be available to more than a few expert users. Such a situation arose in an epidemiological study to estimate the effect of clinical mastitis, where implementation of the currently available algorithm was not clear. The type of solution proposed here is straightforward to implement in this case, as well as in other applications such as estimating the location of cancer clusters relative to toxic waste sites. This new solution will also result in statistically valid conclusions, a property not always enjoyed by computationally intensive procedures. In addition to these algorithms, research in new statistical simulation methods is proposed which has application in genetics and biotechnology studies (the linkage of locations on a chromosome to particular diseases).