Determine an appropriate simulator noise model for RIXS inference

Determine the appropriate noise model for the RIXS simulator, including whether shot noise can be neglected generally or whether Poisson noise augmentation is required for photon-starved measurements.

Background

The simulation-based inference framework currently assumes negligible shot noise when generating RIXS spectra. This assumption may be defensible for the high-count NiPS₃ measurement analyzed in the paper, but it may fail for photon-starved data, where counting statistics can materially affect the inferred Hamiltonian-parameter posterior. Establishing an appropriate simulator noise model, particularly one incorporating Poisson fluctuations when necessary, is therefore unresolved and important for extending the method to lower-count experiments.