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Advancing the Geometric Framework for Computational Statistics: Theory, Methodology and Modern Day Applications

推进计算统计的几何框架：理论、方法论和现代应用

基本信息

批准号：
EP/J016934/2
负责人：
Mark Girolami
金额：
$ 73.12万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ016934%2F2
关键词：
Advancing Geometric Framework Computational Statistics

项目摘要

The vision of this research is to formalise the geometric foundations of computational statistics and provide the tools and analytic results required to realise the ambition of developing the advanced statistical methodology that is essential to address emerging inference problems of major importance across the sciences and industry. As ever more demanding and ambitious applications of existing statistical inference methods are being considered, the capabilities of computational statistics tools are constantly being stretched, often beyond what is practically feasible. For example the potential to gain insights into the mechanisms of cellular function, elucidating ecological dynamics; improving neurological diagnostics, and uncovering the deep mysteries of the cosmos are only some of the ongoing scientific studies that are heavily reliant on statistical inference methods and are placing unparalleled demand on the current capabilities of available statistical methodology. This situation motivates continual innovation in the development of statistical methods for the quantification of uncertainty. The aim of this proposed research is to be more ambitious and go much further in establishing a novel paradigm that underpins the advancement of next generation computational statistical methods by formalising and developing advanced Monte Carlo methods. The geometric foundations of computational statistics will be formalised within this proposed research in a way that reaches beyond traditional interfaces between statistical and mathematical sciences.

本研究的愿景是形式化计算统计学的几何基础，并提供实现开发先进统计方法所需的工具和分析结果，这对于解决科学和工业中重要的新兴推理问题至关重要。随着对现有统计推断方法的要求越来越高、应用越来越广泛，计算统计工具的能力不断得到扩展，往往超出了实际可行的范围。例如，有可能深入了解细胞功能的机制，阐明生态动力学；改进神经学诊断和揭示宇宙的深层奥秘只是正在进行的科学研究的一部分，这些研究严重依赖于统计推断方法，并对现有统计方法的能力提出了前所未有的要求。这种情况促使不确定性量化统计方法的不断创新。这项拟议研究的目的是更加雄心勃勃，并进一步建立一种新的范式，通过形式化和开发先进的蒙特卡罗方法来支持下一代计算统计方法的进步。计算统计学的几何基础将在这个提议的研究中以一种超越统计和数学科学之间传统接口的方式形式化。