Towards a Geometric Characterization of Multiverse Analysis

Abstract

Multiverse analysis makes explicit how empirical conclusions depend on alternative, defensible analytical specifications. Standard approaches usually generate the multiverse first and then summarize it through decision tables, specification curves, model weights, or scalar outputs such as estimates and \textit{p}-values. This stagewise view is useful, but it can hide how inferential uncertainty is arranged across specifications. We propose a distributional-geometric framework in which each admissible specification is represented by a probability distribution on a common target-output space. After defining a suitable distance between these distributions, the induced geometry allows the multiverse of analyses to be studied through local neighbourhoods, diameters, Fréchet barycentres, and dispersion measures. Numerical examples alongside a real case study illustrate how the approach complements existing multiverse summaries by retaining both effect variation and uncertainty variation.