Statistical inference when both the model and/or data dimension is large

本课题主要研究高维复杂数据的推理问题。识别图形模型II.对变量赋予解释能力III.非参数贝叶斯过程的频率主义行为IV.粒子滤波器框架是非参数和半参数的，结果将是渐近的。但是所获得的定性见解已经导致研究人员发现新方法，并且应该再次这样做。21世纪世纪几乎所有领域的数据的一个突出特点是它们的复杂性，图像可以被看作是具有数千维的向量，气候模型产生的向量给出了数万个位置的预测值，基因组有30亿个碱基对长。伴随着这类数据的是它们产生的模型的缺乏。对于这种情况有什么理论告诉我们，如果没有不可能的大量碱基对，我们应该无法做任何事情。然而，我们相信，如果我们考虑预测，模型是“稀疏的”（大多数因素是不相关的）或数据是“稀疏的”（重要的因素是高度依赖的，实际上可以表现得比表面上更复杂）。研究人员正在研究这些基本思想，并开发适用于气候建模，基因组学和天文学等背景的模型。

The investigator is studying inference for data which is both high dimensional and complex.The main topics investigated are:I. Identifying graphical modelsII.Ascribing explanatory power to variablesIII.Frequentist behaviour of nonparametric Bayes proceduresIV.Particle filtersThe framework is non and semiparametric and the results will be asymptotic.But the qualitative insights gained have led to the discovery of new methods by the investigator and should do so again.A preeminent feature of 21st century data in almost all fields is their complexity compared to he number of replicates.Images can be viewed as vectors with dimensions in the thousands,climate models produce vectors giving predicted values at tens of thousands of locations ,genomes are 3 billion basepairs long.Accompanying this type of data is a dearth of models for their generation.What theory there is for such situations tells us that we should be unable to do anything without impossibly large numbers of replicates.Yet are coping,we believe because ,if we consider predictions the models are "sparse"(Most factors are irrelevant) or data are "sparse" (The factors which do matter are highly dependent and can in fact be represented much more compactly than is apparent.) The investigator is studying these underlying ideas and developing models which apply in contexts including climate modeling, genomics, and astronomy.