Do Sparsity Promoting Hierarchical Prior Models Plausibly Model Empirical Image Data

1443 

Contributed Abstract 

Poster 

Alexander Strang (1), Yash Dave (2), Brandon Marks (2), Zixun Wang (2), Hannah Chung (2)

(1) University of California, Berkeley, N/A, (2) University of California, Berkeley, Berkeley, CA

Yash Dave  
University of California, Berkeley

Brandon Marks  
University of California, Berkeley

Zixun Wang  
University of California, Berkeley

Hannah Chung  
University of California, Berkeley

Alexander Strang  
University of California, Berkeley

Yash Dave  
University of California, Berkeley

Scale mixtures of normal distributions are a popular family of hierarchical Bayesian models that compromise interpretability, flexibility, and tractability. Recent work has demonstrated that generalized gamma mixtures of normals admit efficient algorithms that allow inference, uncertainty quantification, and hyper-parameter tuning in large, sparse, ill-determined inverse problems. We demonstrate parameter choices that produce popular prior families (Gaussian, Laplace, Student-t), and relate the distinguishability of priors to level sets of low-order moments in the parameter space using the KL and KS distances for power and significance respectively. We test the empirical validity of the hierarchical priors in a series of large imaging data sets. As case studies, we consider benchmark remote sensing, MRI, and image segmentation data sets. We report plausible ranges of parameters under standard representations (Fourier, wavelet, etc.). We find that, relative to the data sets tested, previous computational work has focused on an overly narrow subset of the space of available priors.

Bayesian hierarchical models|Sparse inference|Image data|Scale mixture models|Compressed sensing|Model validation

Section on Bayesian Statistical Science

Applications in Applied Sciences