Efficiently sample from posterior using DCPS for denoising diffusion priors.
Efficient Multilevel MCMC method for solving Bayesian inverse problems in Navier-Stokes equations with Lagrangian observations.
This paper proposes a data-adaptive prior based on Reproducing Kernel Hilbert Space (RKHS) for Bayesian learning of kernels in operators, addressing the instability of posterior mean in traditional Bayesian methods with non-degenerate priors, particularly in the small noise regime.