权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Information geometry for Bayesian hierarchical models

贝叶斯分层模型的信息几何

基本信息

批准号：
EP/K005723/1
负责人：
Simon Byrne
金额：
$ 30.27万
依托单位：
University College London
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FK005723%2F1
关键词：
Information geometry Bayesian hierarchical models

项目摘要

Modern society is deluged by data. We systematically digitally record and store everything from the seemingly mundane, such as search engine queries, to the valuable and important, such as health care records. The volume of recorded data is only set to increase as technologies such as personalised genome sequencing, which records the six billion base pairs that make up each individual's genome, become commonplace. The challenge for statisticians is to convert this torrent of data into useful and useable information.Statistics is usually taught as a collection of disparate prescriptive techniques-t-tests, analysis of variance, time series, etc.-which can give the impression that each statistical problem falls nicely into one of these categories. Of course this is false: every practical problem has its own particular features, and failing to take these into account can lead to biased or misleading conclusions.In recent years, a more powerful analytical approach has been developed, known as Bayesian hierarchical modelling. These models are constructed in a modular fashion, each component chosen to accurately represent pertinent features of the statistical problem, which are then built into a larger model, forming a hierarchy. As a result, the model is specifically tailored to the problem at hand, leading to more accurate inferences and predictions. Hierarchical models have been applied with great success in a wide variety of areas, including identifying the complicated factors that affect voter behaviour in political science, instrument calibration in engineering, ecological modelling of species populations, and the monitoring and predicting of outcomes in healthcare policy.However, as these models get larger and more detailed, the calculations required to implement them become increasingly complicated and computationally intensive. The aim of this fellowship is to develop theory and methods to make hierarchical modelling feasible for larger and more complex situations.I will apply the mathematical tools and techniques of curvature, known as differential geometry, by interpreting the model as a smooth curved surface called a manifold-think of a rubber sheet that has been twisted, poked and pulled in different places. These computational difficulties then correspond to regions of this surface that are highly curved. I can then adapt various techniques that have been developed for related geometric problems, such as numerical Hamiltonian integrators, in order to construct efficient algorithms that twist, poke and pull this surface into a shape that is more amenable to computation.This research will provide both theoretical developments on which other statisticians can build, as well as practical tools and techniques which applied researchers will be able to use. Such advances will help change our current "data age" into a true "information age".

现代社会充斥着数据。我们系统地以数字方式记录和存储一切，从看似平凡的内容（如搜索引擎查询）到有价值和重要的内容（如医疗记录）。随着个性化基因组测序等技术的普及，记录数据的数量只会增加，个性化基因组测序记录了构成每个人基因组的60亿个碱基对。统计学家面临的挑战是如何将大量的数据转化为有用的信息。统计学通常是作为一系列不同的规范性技术的集合来教授的，如t检验、方差分析、时间序列等。这会给人一种印象，即每个统计问题福尔斯都很好地属于这些类别之一。这当然是假的：每一个实际问题都有其自身的特点，如果不考虑这些特点，可能会导致有偏见或误导性的结论。2近年来，一种更强大的分析方法被发展起来，称为贝叶斯分层模型。这些模型是以模块化的方式构建的，每个组件都被选择来准确地表示统计问题的相关特征，然后将其构建成一个更大的模型，形成一个层次结构。因此，该模型是专门针对手头的问题，从而导致更准确的推断和预测。分层模型已经在许多领域取得了巨大的成功，包括在政治学中识别影响选民行为的复杂因素，工程中的仪器校准，物种种群的生态建模，以及医疗保健政策结果的监测和预测。然而，随着这些模型越来越大，越来越详细，实现它们所需的计算变得越来越复杂和计算密集。这个奖学金的目的是发展理论和方法，使分层建模适用于更大和更复杂的情况。我将应用数学工具和曲率技术，称为微分几何，通过将模型解释为一个光滑的曲面称为流形-想象一个橡胶片，它在不同的地方被扭曲，戳和拉。这些计算困难则对应于该表面的高度弯曲的区域。然后，我可以适应各种技术，已开发的相关几何问题，如数值哈密顿积分，以构建有效的算法，扭曲，戳和拉这个表面成一个形状，更适合计算。这项研究将提供理论发展的基础上，其他统计学家可以建立，以及实用的工具和技术，应用研究人员将能够使用。这些进步将有助于将我们目前的“数据时代”转变为真正的“信息时代”。