Related papers: Multi-fidelity No-U-Turn Sampling

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Markov chain Monte Carlo (MCMC) methods are widely used in machine learning. One of the major problems with MCMC is the question of how to design chains that mix fast over the whole state space; in particular, how to select the parameters…

Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…

A new Micro-Macro-Surrogate (MMS) hybrid method is presented that couples the Direct Simulation Monte Carlo (DSMC) method with Computational Fluid Dynamics (CFD) to simulate low-speed rarefied gas flows. The proposed MMS method incorporates…

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC)…

The Metropolis-Hastings (MH) algorithm is the prototype for a class of Markov chain Monte Carlo methods that propose transitions between states and then accept or reject the proposal. These methods generate a correlated sequence of random…

Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…

Minimization of a stochastic cost function is commonly used for approximate sampling in high-dimensional Bayesian inverse problems with Gaussian prior distributions and multimodal posterior distributions. The density of the samples…

We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the…

Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive…

We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…

The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…

Delayed-acceptance Markov chain Monte Carlo (DA-MCMC) samples from a probability distribution via a two-stages version of the Metropolis-Hastings algorithm, by combining the target distribution with a "surrogate" (i.e. an approximate and…

Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…

The computational cost of traditional first-principles method quickly becomes prohibitively expensive as the number of atoms increases. This challenge is further amplified by the need to evaluate finite-temperature properties with Monte…

In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased…