Related papers: Efficient Gaussian Sampling for Solving Large-Scal…

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not…

In this paper, a novel method to adaptively approximate the solution to stochastic differential equations, which is based on compressive sampling and sparse recovery, is introduced. The proposed method consider the problem of sparse…

We consider the theoretical analysis of Multiscale Sampling Methods, which are a new class of gradient-free Markov chain Monte Carlo (MCMC) methods for high dimensional inverse differential equation problems. A detailed presentation of…

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical…

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…

The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…

The computational complexity of MCMC methods for the exploration of complex probability measures is a challenging and important problem. A challenge of particular importance arises in Bayesian inverse problems where the target distribution…

Markov Chain Monte Carlo (MCMC) sampling methods are widely used but often encounter either slow convergence or biased sampling when applied to multimodal high dimensional distributions. In this paper, we present a general framework of…

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary…

Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…

This work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian…

Sampling from the lattice Gaussian distribution plays an important role in various research fields. In this paper, the Markov chain Monte Carlo (MCMC)-based sampling technique is advanced in several fronts. Firstly, the spectral gap for the…

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…