Related papers: Conditioning by Projection for the Sampling from P…

The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

In this article we consider likelihood-based estimation of static parameters for a class of partially observed McKean-Vlasov (POMV) diffusion process with discrete-time observations over a fixed time interval. In particular, using the…

In this work, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an…

We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation given noisy observation data on its solution at a set of spatial points. We study approximation of the posterior probability…

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…

Markov Chain Monte Carlo (MCMC) algorithms are frequently used to perform inference under a Bayesian modeling framework. Convergence diagnostics, such as traceplots, the Gelman-Rubin potential scale reduction factor, and effective sample…

We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…

We can directly sample from the conditional distribution of any log-affine model. The algorithm is a Markov chain on a bounded integer lattice, and its transition probability is the ratio of the UMVUE (uniformly minimum variance unbiased…

We present an original simulation-based method to estimate likelihood ratios efficiently for general state-space models. Our method relies on a novel use of the conditional Sequential Monte Carlo (cSMC) algorithm introduced in…

Bayesian computation of high dimensional linear regression models with a popular Gaussian scale mixture prior distribution using Markov Chain Monte Carlo (MCMC) or its variants can be extremely slow or completely prohibitive due to the…

Bayesian methods have proven themselves to be successful across a wide range of scientific problems and have many well-documented advantages over competing methods. However, these methods run into difficulties for two major and prevalent…

Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability…

In this paper we propose an algorithm for recovering sparse orthogonal polynomials using stochastic collocation. Our approach is motivated by the desire to use generalized polynomial chaos expansions (PCE) to quantify uncertainty in models…

A typical Bayesian inference on the values of some parameters of interest $\bf q$ from some data $D$ involves running a Markov Chain (MC) to sample from the posterior $p({\bf q},{\bf n} | D) \propto \mathcal{L}(D | {\bf q},{\bf n}) p({\bf…

This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly…

This work considers the problem of sampling from a probability distribution known up to a normalization constant while satisfying a set of statistical constraints specified by the expected values of general nonlinear functions. This problem…