Bayesian Inference using the Proximal Mapping: Uncertainty Quantification under Varying Dimensionality

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 the 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

Keywords:

• Computer science
• Random variable
• Algorithm
• Probabilistic logic
• Uncertainty quantification
• Bayesian probability
• Bayesian inference
• Posterior probability
• Frequentist inference
• Point estimation

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