Principled inference for functionals of large structured covariance matrices.

大型结构化协方差矩阵泛函的原则推理。

• 批准号: EP/P002757/1
• 负责人: Heather Battey
• 金额: $ 41.74万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FP002757%2F1
• 关键词: Principled; inference; functionals; large; structured

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.

统计在日常生活中发挥着重要作用，通过更好地理解支撑我们观察到的数据的科学或社会真相，可以更好地针对昂贵的医疗筛查、药物开发、营销活动或政府监管。越来越频繁地，我们希望了解的科学真理对应于高维参数。该项目考虑协方差矩阵和相关量，如逆协方差矩阵，这是特别重要的高维参数类型，在许多统计应用中出现。当协方差矩阵的维度大于可用数据点的数量时，必须假设结构（某些域中的稀疏性），以便获得统计上表现良好的估计值。本计画探讨协方差与逆协方差矩阵估计的新结构类型。这些结构中的一些便于关于真实高维参数的不确定性陈述，而不是简单地提供点估计。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数。

项目成果

On sparsity scales and covariance matrix transformations

• DOI: 10.1093/biomet/asz014
• 发表时间: 2019-09
• 期刊: Biometrika
• 影响因子: 2.7
• 作者: H. Battey

A note on the analytic approximation of exceedance probabilities in heterogeneous populations

关于异质群体中超越概率的解析近似的注解

• DOI: 10.1016/j.spl.2021.109215
• 发表时间: 2021
• 期刊: Statistics & Probability Letters
• 影响因子: 0.8
• 作者: Battey H

HCmodelSets: An R Package for Specifying Sets of Well-fitting Models in High Dimensions

HCmodelSets：用于指定高维度拟合良好模型集的 R 包

• DOI: 10.32614/rj-2019-057
• 发表时间: 2019
• 期刊: The R Journal
• 作者: Hoeltgebaum H

Large numbers of explanatory variables: a probabilistic assessment.

• DOI: 10.1098/rspa.2017.0631
• 发表时间: 2018-07
• 期刊: Proceedings. Mathematical, physical, and engineering sciences
• 作者: Battey HS;Cox DR
• 通讯作者: Cox DR

Data and variables from On the linear in probability model for binary data.

数据和变量来自二进制数据的线性概率模型。

• DOI: 10.6084/m9.figshare.8025896
• 发表时间: 2019
• 作者: H. S. Battey