Importance sampling is used to approximate Bayes' rule in many computational approaches
to Bayesian inverse problems, data assimilation and machine learning. This paper reviews …

Ensemble Kalman inversion (EKI) is an adaption of the ensemble Kalman filter (EnKF) for
the numerical solution of inverse problems. Both EKI and EnKF suffer from the'subspace …

Integrative methods for post-selection inference under convex constraints Page 1 The Annals
of Statistics 2021, Vol. 49, No. 5, 2803–2824 https://doi.org/10.1214/21-AOS2057 © Institute of …

A unified performance analysis of likelihood-informed subspace methods Page 1 Bernoulli
28(4), 2022, 2788–2815 https://doi.org/10.3150/21-BEJ1437 A unified performance analysis …

The Gibbs sampler (aka Glauber dynamics and heat-bath algorithm) is a popular Markov
Chain Monte Carlo algorithm which iteratively samples from the conditional distributions of a …

Gradient descent (GD) is known to converge quickly for convex objective functions, but it can
be trapped at local minima. On the other hand, Langevin dynamics (LD) can explore the …

For two probability measures ρ and π with analytic densities on the d-dimensional cube [-1,
1] d, we investigate the approximation of the unique triangular monotone Knothe–Rosenblatt …

Ensemble forecast based on physics-informed models is one of the most widely used
forecast algorithms for complex turbulent systems. A major difficulty in such a method is the …

We consider Bayesian inference for image deblurring with total variation (TV) prior. Since
the posterior is analytically intractable, we resort to Markov chain Monte Carlo (MCMC) …

For two probability measures ρ and π on [-1, 1] N we investigate the approximation of the
triangular Knothe–Rosenblatt transport T:[-1, 1] N→[-1, 1] N that pushes forward ρ to π …