Gaussian likelihood of flattened persistence-image vectorization

Ascertain whether a data vector formed by flattening and concatenating persistence images of the persistent homology outputs for halo catalogs has an approximately Gaussian likelihood, in order to validate the use of Fisher-matrix forecasting based on this representation.

Background

The authors discuss vectorization choices for persistent homology outputs, including flattening persistence images versus constructing histogram-based summaries. Their Fisher-analysis pipeline assumes a Gaussian likelihood for the data vector.

They explicitly note uncertainty regarding whether a flattened persistence-image vectorization yields a Gaussian likelihood, which impacts the applicability of standard Fisher forecasting methods.