Bayesian Inference Using the Proximal Mapping: Uncertainty Quantification Under Varying Dimensionality

Maoran Xu, Hua Zhou, Yujie Hu and Leo L. Duan

Journal of the American Statistical Association, 2024, vol. 119, issue 547, 1847-1858

Abstract: In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of obtaining a point estimate via optimization, it is much more challenging to quantify their uncertainty. In the Bayesian framework, a major difficulty is that if assigning the prior associated with a p-dimensional measure, then there is zero posterior probability on any lower-dimensional subset with dimension d

Date: 2024
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DOI: 10.1080/01621459.2023.2220170

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