Causal Inference from Partial Statistical Information

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Much of statistical theory is concerned with the analysis of a singledata set, obtained from an experiment, survey, or study. However inmany fields which most urgently demand new statistical methodology,problems do not fit this paradigm. Instead data are gathered frommultiple settings under different experimental conditions, which maymeasure different variables or be sampling from differentpopulations. This leads to situations in which it is unclear how tocombine statistical information in a way that provides a coherentsolution agreeing with all studies, and which properly quantifies theuncertainty in the estimation process.The gold-standard method for answering causal questions is therandomised controlled trial (RCT), but RCTs are extremely expensiveand usually end without a positive result. Meanwhile biology andmedicine are at the forefront of the big data revolution, as more andmore is being measured at greater and greater resolutions; the 100,000Genomes Project and UK Biobank each contain tens of thousands ofgenetic and phenotypic measurements on hundreds of thousands ofpeople. Electronic healthcare records will generate Terabytes ofmedical information about tens of millions of people. Many of thequantities measured in these data sets cannot be experimentallycontrolled for practical, financial or ethical reasons.This project aims to uncover how much we can learn about the causalmechanisms underlying multiple large and complex data sets withoutperforming experiments, or with limited experimental data: to learn as much as possible about the world just by looking.