Sensitivity analysis in statistical science studies how scientifically relevant changes in the way we formulate problems affect answers to our questions of interest. New advances in statistical geometry allow us to build a rigorous framework in which to investigate these problems and develop insightful computational tools, including new diagnostic measures and plots.

This talk will be about statistical model elaboration using sensitivity analysis aided with geometry. Throughout we assume there is a working parametric model. The key idea here is to explore discretisations of the data, at which point multinomial distributions become universal (all possible models are cov- ered). The resulting structure is well-suited to discussing practically important statistical topics, such as exponential families and generalised linear models. The theory of cuts in exponential families allows clean inferential separation between interest and nuisance parameters and provides a basis for appropriate model elaboration. Examples are given where the resulting sensitivity analyses indicate the need for specific model elaboration or data re-examination.