Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.
A computational framework for infinite-dimensional Bayesian inverse problems Part I: The linearized case, with application to global seismic inversion
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Constraint residuals, graph posteriors, and determinant-corrected full-space targets in Bayesian inverse problems
Uncorrected Gaussian residual penalties in full-space sampling converge after marginalization to the graph-lifted reduced posterior multiplied by the inverse absolute determinant of the state Jacobian, requiring explicit determinant corrections for equivalence.