Towards a Geometric Characterization of Multiverse Analysis

2026-07-13

AI Summary

Traditional multiverse analyses struggle to characterize the structure of inferential uncertainty across different analytical specifications. This work proposes a distribution–geometry framework that models each plausible analysis specification as a probability distribution over the target outcome space and constructs a geometric structure based on distances between these distributions, thereby introducing a geometric perspective to dissect effect heterogeneity and uncertainty variation for the first time. The framework leverages geometric tools—such as neighborhoods, diameters, Fréchet means, and dispersion measures—to effectively preserve and reveal variability inherent in the multiverse of analyses. Numerical experiments and real-world case studies demonstrate that this approach substantially complements existing summarization strategies, enhancing analytical depth while retaining fine-grained details of both effect estimates and their associated uncertainties.

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.

Problem

• multiverse analysis
• inferential uncertainty
• analytical specifications
• distributional geometry
• effect variation

Innovation

• multiverse analysis
• distributional geometry
• Fréchet barycentre
• inferential uncertainty
• specification space