"Bayesian inference, model checking, prior-data conflict, and inferences via Bayes factors and relative belief ratios"

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This research is concerned with developing statistical methodology for model checking, checking for prior-data conflict, selection of priors and invariant methods for statistical inference. Applications are made to practical problems in statistical genetics, marketing, machine learning and population health studies. Statistical analyses are dependent upon choices made by an analyst. These choices include the sampling model to describe the generation of observed data and the choice of a prior that describes uncertainties about the true distribution within the sampling model. In both cases these choices are made subjectively. While such choices should be made based upon one's best judgement, a basic principle is that such choices should be checked against the objective data to ensure that they make sense. Model checking is a common statistical activity but checking for prior-data conflict is not. At least part of the reason for this is the ambiguity about what to do when such a conflict exists. This research is concerned with how to select priors for particular classes of problems, such as logistic regression and structural equation modelling, how to assess whether or not prior-data conflict exists and what to do when this occurs. Another basic principle concerns invariance. When an analyst makes a choice that cannot be checked against the data, then it is natural to require that the analysis be invariant under the choice made. The choice of a particular representation of the data and the parameterization of a statistical model are examples of such choices. Another aspect of this research is concerned with developing the theoretical and practical implementational aspects of Bayesian methodology that is invariant under such choices for model checking, checking the prior and for inference based on a given model and prior.