Doctors and epidemiologists are drowning in data from wearables, genetic tests, and medical scans, but the statistical tools needed to turn that flood of information into reliable decisions for individual patients do not yet exist. The core problem is uncertainty: a drug that works for most people might kill one in a thousand, and current machine learning methods are poor at quantifying such rare but critical risks. Bayesian statistics is designed to handle exactly this kind of uncertainty, but its traditional methods are too computationally expensive for modern big-data health applications. This research will develop new, faster Bayesian approaches—building on recent breakthroughs in Monte Carlo integration and targeted model updates—that can run on large datasets without sacrificing the rigorous uncertainty quantification that medical decisions demand. If successful, the work could enable real-time patient monitoring, personalised treatment plans, and more robust epidemic response systems, all while ensuring that decisions are driven by the probability of rare but serious events rather than by averages.
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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.
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