Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with Non-Gaussian Noise

Abstract Likelihood analysis is typically limited to normally distributed noise due the difficulty of determining probability density function complex, high-dimensional, non-Gaussian, and anisotropic noise. This a major limitation for precision measurements in many domains science, including astrophysics, example, cosmic microwave background, gravitational waves, lensing, exoplanets. work presents Score-based LIkelihood Characterization, framework that resolves this issue by building data-driven model using set realizations from observations. We show approach produces unbiased precise likelihoods even presence highly non-Gaussian correlated spatially varying use diffusion generative models estimate gradient with respect data elements. In combination Jacobian physical signal, we Langevin sampling produce independent samples likelihood. demonstrate effectiveness method real Hubble Space Telescope James Webb Telescope.