New Approaches to Bayesian Data Science: Tackling Challenges from the Health Sciences

健康科学在个人和人口层面上收集的数据量呈爆炸式增长。这些数据可以是多种多样的，包括遗传信息、健康记录、从可穿戴设备获得的活动水平数据以及扫描产生的图像数据。如果我们能从这些数据中充分理解，就有巨大的潜力改进诊断、及时干预和更有效的治疗。示例应用包括实时监测患者、开发个性化治疗或流行病的实时监测和决策。然而，提取这些见解的数据科学挑战是巨大的。这些挑战的特点包括需要对群体中的个人做出推断和决策，以及需要综合来自不同数据源和数据类型的信息。虽然我们在人口水平上收集了大量数据，但任何特定个人的信息数量可能仍然有限。适当地量化不确定性对于决策至关重要，最佳决策通常是由相对罕见事件（例如对药物的极端反应）的概率驱动的。我们需要基于模型的数据科学方法，可以利用科学理解，但我们需要统计分析对这些模型不可避免的不足进行稳健处理。这些应用的基础是开发新的理解，这与当前统计或机器学习方法中最常见的预测不同。贝叶斯数据科学为解决这些挑战提供了一个自然的框架。贝叶斯方法是基于模型的，可以适当地量化和传播不确定性，并且通过分层模型可以在对个体进行推断时使用群体水平的信息。贝叶斯定理的重复应用为跨多个数据源的信息综合提供了一种自然的范式。然而，目前的贝叶斯数据科学方法对于健康科学中的许多现代大数据应用并不可行。贝叶斯方法需要对不确定性进行积分。与其他通常基于优化的数据科学方法相比，这种高维集成带来了大量的计算开销。因此，虽然贝叶斯分析的动机是明确的，但这种计算开销意味着，目前实现贝叶斯方法通常是不可行的。该研究方案将开发新的贝叶斯数据科学方法，这些方法在健康科学和更广泛的领域都是需要的。它建立在蒙特卡罗集成方法的最新突破之上，该方法显示出对大数据高效的巨大希望；以及适用于复杂模型的类贝叶斯更新的新范式，这些新范式只将建模工作集中在这些模型中最重要的方面。它将解决健康科学中的关键研究挑战——直接为这些挑战开发新的见解和理解。

The health sciences have seen an explosion in the amount of data collected at both individual and population levels. This data can be varied, including genetic information, health records, data on activity levels obtained from wearable devices, and image data from scans. There is huge potential for improved diagnoses, timely interventions and more effective treatments if we can fully extract understanding from this data. Example applications included real-time monitoring of patients, developing personalised treatment, or real-time monitoring and decision-making for epidemics. However the data science challenges in extracting these insights are vast.Features of these challenges include the need to make inferences about and decisions for individuals from within a population, and the need to synthesise information from disparate data sources and data types. Whilst we have substantial data collected at a population level, the amount of information on any given individual may be still be limited. Appropriately quantifying uncertainty is crucial for making decisions, with the optimal decision often being driven by the probability of relatively rare events (e.g. extreme reaction to a drug). We need model-based approaches to data science that can leverage scientific understanding, but we need the statistical analyses to be robust to unavoidable inadequacies of these models. Underpinning many of these applications is the requirement to develop new understanding, and this differs from a focus on making predictions that it is most common among current statistical or machine learning methods. Bayesian data science provides a natural framework for tackling these challenges. Bayesian methods are model-based, can appropriately quantify and propagate uncertainty, and through hierarchical models are able to use population-level information when making inferences about individuals. Repeated application of Bayes theorem gives a natural paradigm for synthesizing information across multiple data sources. However, current Bayesian data science methods are not feasible for many modern, big-data, applications in the health sciences. Bayesian methods require integrating over uncertainty. Such high-dimensional integration carries a substantial computational overhead when compared to alternative, often optimization-based, data science methods. So while the motivation for Bayesian analysis is clear, this computational overhead means that, currently, implementing Bayesian approaches is often not feasible. This programme of research will develop the new approaches to Bayesian data science that are needed both within the health sciences and more widely. It builds on recent breakthroughs in Monte Carlo integration methods that show great promise for being efficient for large data; and on new paradigms for Bayesian-like updates that are suitable for complex models and which focus modelling effort just on the aspects of these models that are most important. It will address key research challenges in the health sciences -- directly developing new insights and understanding for these.