Recent decades have seen enormous improvements in computational inference for
statistical models; there have been competitive continual enhancements in a wide range of …

Based on the parametric deterministic formulation of Bayesian inverse problems with
unknown input parameter from infinite-dimensional, separable Banach spaces proposed in …

We present a parametric deterministic formulation of Bayesian inverse problems with an
input parameter from infinite-dimensional, separable Banach spaces. In this formulation, the …

Statistical models with constrained probability distributions are abundant in machine
learning. Some examples include regression models with norm constraints (eg, Lasso) …

The availability of datasets with large numbers of variables is rapidly increasing. The
effective application of Bayesian variable selection methods for regression with these …

The problem of sampling constrained continuous distributions has frequently appeared in
many machine/statistical learning models. Many Markov Chain Monte Carlo (MCMC) …

One main limitation of the existing optimal scaling results for Metropolis–Hastings algorithms
is that the assumptions on the target distribution are unrealistic. In this paper, we consider …

We establish posterior sparsity in Bayesian inversion for systems governed by operator
equations with distributed parameter uncertainty subject to noisy observation data δ. We …

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC)
algorithms to the computer science notion of algorithm complexity. Our main result states …

Abstract We consider the Random Walk Metropolis algorithm on R^n with Gaussian
proposals, and when the target probability measure is the n-fold product of a one …