Artificial and Approximate Likelihoods

DMS 9626266 Mykland 该项目旨在将似然方法的使用扩展到半参数和非参数情况。 重要的问题包括如何定义和评估似然比和R星统计量的准确性。 特别感兴趣的是迄今为止的发展的双重可能性，巴特利特身份的鞅，和嵌入技术，允许推导渐近展开的鞅。 目前，研究人员正在扩大理论，以涵盖非鞅的情况下，通过考虑标准功能，这是近似的可能性。 这涵盖了更广泛的数据分析问题。 最好能描述什么类型的推论可以被这种方法所涵盖，以及在执行基于这种方法的程序时，应该使用什么样的似然性推论校正。 这项研究涉及现有的程序（如经验和点过程“似然性”），并在新的建设所产生的人工可能性的观点。 特别是，“设计自己的可能性”正在调查，特别是参考restaurant为基础的标准功能。 作为该项目的一部分，正在研究金融工程和不确定性投资问题的影响。 企业和政府的决策者都面临着在不确定性下做出决策的需要。 例如，企业在对产品当前和未来市场状况不完全了解的情况下投资新工厂。 另一个例子是，有关环境的规章往往试图影响非常复杂的系统，即使有最好的模型和科学研究，人们的行动的影响也存在巨大的不确定性。 在这种情况下，决策不仅需要估计和预测，而且还需要最准确地量化这些估计与实际数字之间的差距。 这个项目是关于一种新的技术，它可以大大提高这种评估的可靠性。 它基于一种统计理论（“似然推断”），这种理论最早于20世纪20年代在英国发展起来，但直到最近几年才被开放给决策者经常面对的更复杂和模糊的系统。

DMS 9626266 Mykland The project seeks to extend the use of likelihood methods to semi- and nonparametric situations. Important questions include how to define and assess the accuracy of the likelihood ratio and R-star statistics. Of particular interest so far has been the development of the dual likelihood, of Bartlett identities for martingales, and of embedding techniques which permit the derivation of asymptotic expansions for martingales. Currently, the investigators are expanding the theory to cover non-martingale situations, by considering criterion functions which are approximately likelihoods. This covers a much broader spectrum of data analysis problems. It is desirable to describe what types of inference can be covered by this, and what corrections over likelihood inference that ought to be used when carrying out procedures based on this approach. The study concerns both existing procedures (such as empirical and point process "likelihoods"), and at new constructions which arise from the artificial likelihood point of view. In particular, the "design-your-own likelihood" is being investigated, with particular reference to resampling based criterion functions. The implications for problems in financial engineering and investment under uncertainty are being studied as part of the project. Policy makers in both business and goverment are faced with the need to take decisions under uncertainty. Firms invest in new plants, for instance, with imperfect knowledge of current and future market conditions for their products. Regulations concerning the environment, as another example, often try to affect systems that are so complex that even with the best models and scientific studies, there is tremendous uncertainty about the effects of one's actions. Decisions in such circumstances not only require estimates and predictions, but also a maximally accurate quantification of how far away such estimates are likely to be from the actual figures. This project is about a new technology for doing this, one that substantially improves the reliability of such assessments. It is based on a statistical theory ("likelihood inference") first developed in Britain in the 1920s, but which has only in the last few years been opened up to the more complex and vaguely specified systems often faced by policy makers.