标题： 超越高斯噪声：非高斯噪声下的似然分析的广义方法 显示英文标题

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

摘要： 似然分析通常仅限于正态分布的噪声，这是由于确定复杂、高维、非高斯和各向异性噪声的概率密度函数具有难度。 这对于科学多个领域的精密测量是一个主要限制，例如在天体物理学中，对于宇宙微波背景的分析、引力波、引力透镜和系外行星的分析。 这项工作提出了 基于分数的似然表征（SLIC），一种通过使用观察结果的一组噪声实现来构建数据驱动的噪声模型的框架。 我们证明了该方法即使在高度非高斯相关和空间变化的噪声存在的情况下，也能产生无偏且精确的似然。 我们使用扩散生成模型来估计噪声的概率密度相对于数据元素的梯度。 结合信号的物理模型的雅可比矩阵，我们使用 Langevin采样从无偏似然中产生独立样本。 我们使用哈勃 空间望远镜和詹姆斯·韦布空间望远镜的真实数据来展示该方法的有效性。 显示英文摘要

摘要： 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.