Principled inference for functionals of large structured covariance matrices.

统计在日常生活中发挥着重要作用，通过更好地了解我们观察到的数据背后的科学或社会真相，可以使昂贵的医疗筛查、药物开发、营销活动或政府监管更有针对性。我们希望学习的科学真理越来越多地与高维参数相对应。本项目考虑了协方差矩阵和相关的量，如逆协方差矩阵，这是在许多统计应用中出现的特别重要的高维参数类型。当协方差矩阵的维数大于可用数据点的数量时，为了获得统计上表现良好的估计，必须假设结构（某些域的稀疏性）。本项目探索了协方差和逆协方差矩阵估计的新型结构。其中一些结构促进了对真实高维参数的不确定性陈述，而不是简单地提供一个点估计。它们还允许在不损失统计准确性的情况下汇总不同的估计。

Statistics plays a fundamental role in daily life, allowing costly medical screening, drug development, marketing campaigns or government regulation to be better targeted through improved understanding of the scientific or societal truths underpinning the data we observe. More and more frequently, the scientific truths we wish to learn correspond to a high dimensional parameter. This project considers covariance matrices and related quantities such as inverse covariance matrices, which are particularly important types of high dimensional parameter, arising in numerous statistical applications. When the dimensionality of the covariance matrix is larger than the number of available data points, structure (sparsity in some domain) must be assumed in order to obtain estimates that are well behaved statistically. This project explores new types of structure for covariance and inverse covariance matrix estimation. Some of these structures facilitate uncertainty statements about the true high dimensional parameter rather than simply providing a point estimate. They also allow different estimates to be aggregated without losing statistical accuracy.