# Do Generalized-Gamma Scale Mixtures of Normals Fit Large Image Datasets? Source: [Do Generalized-Gamma Scale Mixtures of Normals Fit Large Image Datasets?]() Collection index: [llms.txt]() Data updated: 2026-04-14T05:00:11.146Z Authors: Brandon Marks, Yash Dave, Zixun Wang, Hannah Chung, Riya Patwa, Simon Cha, Michael Murphy, Alexander Strang Published: 2025-12-18T20:01:44.000Z ## Abstract A scale mixture of normals is a distribution formed by mixing a collection of normal distributions with fixed mean but different variances. A generalized gamma scale mixture draws the variances from a generalized gamma distribution. Generalized gamma scale mixtures of normals have been proposed as an attractive class of parametric priors for Bayesian inference in inverse imaging problems. Generalized gamma scale mixtures have two shape parameters, one that controls the behavior of the distribution about its mode, and the other that controls its tail decay. In this paper, we provide the first demonstration that the prior model is realistic for multiple large imaging data sets. We draw data from remote sensing, medical imaging, and image classification applications. We study the realism of the prior when applied to Fourier and wavelet (Haar and Gabor) transformations of the images, as well as to the coefficients produced by convolving the images against the filters used in the first layer of AlexNet, a popular convolutional neural network trained for image classification. We discuss data augmentation procedures that improve the fit of the model, procedures for identifying approximately exchangeable coefficients, and characterize the parameter regions that best describe the observed data sets. These regions are significantly broader than the region of primary focus in computational work. We show that this prior family provides a substantially better fit to each data set than any of the standard priors it contains. These include Gaussian, Laplace, $\\ell\_p$, and Student's $t$ priors. Finally, we identify cases where the prior is unrealistic and highlight characteristic features of images that suggest the model will fit poorly. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()