★ Simulation-Based Homotopy: Stress-Testing Gravitational-Wave Posteriors ★

About

We present a framework for probing the full geometry of Bayesian posteriors in inverse problems through a noise-conditioned homotopy. By embedding the likelihood in a one-parameter family controlled by a noise-scaling parameter, we construct a continuous deformation from an almost deterministic posterior concentrated at the true parameters to the full noisy posterior. Traversing this path reveals how posterior structure evolves with measurement quality: when multi-modality emerges, where Gaussian approximations break down, and how parameter degeneracies develop. We argue this constitutes a more integrated alternative to Fisher-information analyses, which becomes beneficial especially in multimodal geometries.

Additionally, deviations from smooth homotopy behaviour provide direct diagnostics of inference pipelines, allowing identification of spurious correlations, mode-collapse artefacts, and approximation breakdowns. We discuss the framework as a general validation and benchmarking tool for simulation-based inference methods.

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