Fast Updating of Bayesian Models

贝叶斯模型的快速更新

• 批准号: 2605897
• 金额: --
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2605897
• 关键词: Fast; Updating; Bayesian; Models

Bayesian inference provides a powerful tool for modelling complex data and quantifying uncertainty, and has been used to solve problems in many areas including epidemiology, climatology, signal process-ing, to name a few. In the applications of Bayesian inference, a common requirement is the ability to update Bayesian models quickly. This is especially desired when, for example, building models iteratively to reflect a change in the prior beliefs, to incorporate new observations into the model, or to correct the model after rectication of old data. A concrete example is in epidemiological modelling of the COVID-19 transmission, where a Bayesian model is built to predict the daily coronavirus cases, and new posterior fits are required every day as new data are collected and fed into the model. Another example is model development, where practitioners often wish to make adjustments to elements of themodel to account for changes in their prior believes.In this setting, which we term iterative Bayesian modelling, practitioners often have had a posterior sample for the t of the previous model at their disposal, and wish to obtain a new sample for the updated model. The traditional approach to iterative Bayesian modelling is to run a Bayesian inference method from scratch each time the model is updated. Although this can yield state-of-the-art approximation accuracy, it is undesirable since these Bayesian inference methods are often computationally expensive, and the computation spent in fitting the old models would be wasted. Existing literature has provided theoretical results on when re-using old fits could help the fitting of a new model, but this remains an ununified area of research. In this PhD project, we aim to explore different methods that can make use of the t to the old model to accelerate the fitting of the updatedmodel. Some objectives of this project are:1. Designing algorithms that are able to update Bayesian models quickly under assumptions on the form of the changes to the model.2. Reviewing and extending existing Bayesian inference methods to allow re-use of previous fits, and making comprehensive comparisons on their advantages and limitations.3. Unifying the existing literature on the theoretical results of when re-using previous fits can be more beneficial than running a Bayesian method from scratch, thus providing theoretical justificationsto the use of these algorithms in iterative Bayesian modelling.This project falls within the EPSRC research area of Mathematical Sciences. If successful, it can shed light on the development of programming software that allows rapid model updating or modeldevelopment, thereby beneting the wide community of practitioners of Bayesian statistics.1

贝叶斯推理为复杂数据建模和量化不确定性提供了一个强大的工具，并已被用于解决许多领域的问题，包括流行病学，气候学，信号处理等。在贝叶斯推理的应用中，一个常见的需求是能够快速更新贝叶斯模型。例如，当迭代地构建模型以反映先验信念的变化、将新的观察结果并入模型或在重新计算旧数据后校正模型时，这是特别期望的。一个具体的例子是COVID-19传播的流行病学建模，其中构建贝叶斯模型来预测每日冠状病毒病例，并且随着新数据的收集和输入模型，每天都需要新的后验拟合。另一个例子是模型开发，从业者经常希望对模型的元素进行调整，以解释他们先前信念的变化。在这种情况下，我们称之为迭代贝叶斯模型，从业者经常有一个前一个模型的后验样本，并希望为更新后的模型获得一个新的样本。迭代贝叶斯建模的传统方法是在每次更新模型时从头开始运行贝叶斯推理方法。虽然这可以产生最先进的近似精度，但这是不期望的，因为这些贝叶斯推理方法通常在计算上是昂贵的，并且在拟合旧模型中花费的计算将被浪费。现有的文献提供了理论上的结果，当重新使用旧的配合可以帮助拟合一个新的模型，但这仍然是一个不统一的研究领域。在这个博士项目中，我们的目标是探索不同的方法，可以利用旧模型的t来加速更新模型的拟合。该项目的一些目标是：1。设计能够在模型变化形式的假设下快速更新贝叶斯模型的算法。2.回顾和扩展现有的贝叶斯推理方法，允许重用以前的拟合，并对它们的优点和局限性进行全面的比较.统一现有的文献上的理论结果时，重新使用以前的配合可以比从头开始运行贝叶斯方法更有益，从而提供了理论justificationsto使用这些算法在迭代贝叶斯modelling.This项目福尔斯属于EPSRC的数学科学研究领域。如果成功的话，它可以为编程软件的开发提供帮助，从而允许快速模型更新或模型开发，从而使贝叶斯理论的广泛从业者受益。