Bayesian inference and decisions under partial specification

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My proposed research will focus on developing methodology and computational tools to allow the wider use of the Bayesian statistical paradigm in scientific and other research settings. The Bayesian approach allows researchers to make coherent inferences about unknown quantities of interest (eg the magnitude of the effect of a treatment or exposure on an outcome), and also to make optimal decisions in the presence of randomness and uncertainty. Bayesian methodology in its traditional form is bound by quite strict assumptions that limit its applicability, or at least makes quite strong modelling assumptions: this might be viewed as a negative aspect. In addition, Bayesian methods are typically much harder to implement than classical statistical procedures, and often carry a greater computational burden. My goal is to develop the theory, methodology and computational tools to make Bayesian inference more accessible and palatable to researchers. The main direction of the proposed research program is inspired by recent work that has demonstrated that more general 'belief updating' mechanisms exist, beyond the usual Bayesian update, that could allow simpler specifications and computation without losing the advantages of the Bayesian approach (specifically, the fact that inferences are made through probabilistic arguments). My proposed research will involve an investigation of these new methods which have the potential to revolutionize Bayesian thinking. As well as establishing theoretical connections with more standard Bayesian methods, I will study concrete examples of challenging statistical inference settings which would benefit from the development of a new, simpler and more computationally efficient approach. These examples are drawn from my current research interests in causal inference (which aims to identify the unconfounded effect of a treatment or exposure) and phylogenetics (which aims to analyze evolutionary relationships between species or molecular genetic samples), but extend to a new area of my research related to machine learning examples. Machine learning and artificial intelligence (AI) research is of growing importance in all areas of quantitative analysis, and although it is largely dominated by computer science, there is an important role for statisticians to play in validating the models, algorithms and other procedures utilized. My proposed work will contribute in the area of machine learning and AI by studying formal Bayesian procedures, both using the standard Bayesian formulation, and the newly proposed framework.