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

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, 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.

An Ultra Fast Semantic Segmentation Model for AMR’s Path Planning

“…Finally, network parameters are optimized using Adam's optimum function [47][48][49][50][51] with a learning rate of 0.001 and 100 epochs in order to maximize the balanced cross-entropy [52][53][54] described by Equation ( 1). Gaussian blur [55,56] and Gaussian noise [57,58] are applied to the data set as preprocessing to assure the quality of the raw images before they are fed into the suggested segmentation model (see Fig. 4).…”

An Improved Gaussian Sum Extended Kalman Filter With Colored Noise for GNSS/SINS Tightly Coupled Positioning and Attitude Determination Systems

“…Non-Gaussian colored noise not only deviates from a Gaussian distribution, but also exhibits a correlation in time, resulting in colored noise. Non-Gaussian colored noise is commonly encountered in GNSS/SINS tightly coupled positioning and attitude determination systems utilized on UAV operating in challenging environments [15], [16].…”