Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with non-Gaussian Noise
arXiv:2302.03046 · doi:10.3847/2041-8213/acd645
Abstract
Likelihood analysis is typically limited to normally distributed noise due to the difficulty of determining the probability density function of complex, high-dimensional, non-Gaussian, and anisotropic noise. This is a major limitation for precision measurements in many domains of science, including astrophysics, for example, for the analysis of the Cosmic Microwave Background, gravitational waves, gravitational lensing, and exoplanets. This work presents Score-based LIkelihood Characterization (SLIC), a framework that resolves this issue by building a data-driven noise model using a set of noise realizations from observations. We show that the approach produces unbiased and precise likelihoods even in the presence of highly non-Gaussian correlated and spatially varying noise. We use diffusion generative models to estimate the gradient of the probability density of noise with respect to data elements. In combination with the Jacobian of the physical model of the signal, we use Langevin sampling to produce independent samples from the unbiased likelihood. We demonstrate the effectiveness of the method using real data from the Hubble Space Telescope and James Webb Space Telescope.
arXiv comment8 pages, 4 figures
References in corpus (23)
- emcee: The MCMC Hammer
- A guide to LIGO-Virgo detector noise and extraction of transient gravitational-wave signals
- Kepler Mission Stellar and Instrument Noise Properties
- Parameter inference with estimated covariance matrices
- A Fast Algorithm for Cosmic Rays Removal from Single Images
- Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation
- On the assumption of Gaussianity for cosmological two-point statistics and parameter dependent covariance matrices
- JWST Noise Floor I: Random Error Sources in JWST NIRCam Time Series
- Inferring the core-collapse supernova explosion mechanism with gravitational waves
- Detecting Gravitational Waves in Data with Non-Gaussian Noise
- Impact of Simulated 1/f Noise for HI Intensity Mapping Experiments
- deepCR: Cosmic Ray Rejection with Deep Learning
- Probabilistic Mass Mapping with Neural Score Estimation
- Likelihood Non-Gaussianity in Large-Scale Structure Analyses
- On estimating cosmology-dependent covariance matrices
- Cosmological Inference from Galaxy-Clustering Power Spectrum: Gaussianization and Covariance Decomposition
- The impact of cosmic rays on the sensitivity of JWST/NIRSpec
- Flow-Based Likelihoods for Non-Gaussian Inference
- Taming systematic uncertainties at the LHC with the central limit theorem
- Tackling excess noise from bilinear and nonlinear couplings in gravitational-wave interferometers
- A Framework for Obtaining Accurate Posteriors of Strong Gravitational Lensing Parameters with Flexible Priors and Implicit Likelihoods using Density Estimation
- Impact of noise on cosmological parameter constraints for SKA intensity mapping
- Using Cosmic Rays detected by HST as Geophysical Markers I: Detection and Characterization of Cosmic Rays