Related papers: Monte Carlo on manifolds: sampling densities and i…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such random models to obtain statistics on their long-term response.…
Practitioners of Bayesian statistics have long depended on Markov chain Monte Carlo (MCMC) to obtain samples from intractable posterior distributions. Unfortunately, MCMC algorithms are typically serial, and do not scale to the large…
Traditional gradient-based sampling methods, like standard Hamiltonian Monte Carlo, require that the desired target distribution is continuous and differentiable. This limits the types of models one can define, although the presented models…
We consider systems of stochastic differential equations with multiple scales and small noise and assume that the coefficients of the equations are ergodic and stationary random fields. Our goal is to construct provably-efficient importance…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…
Many problems require to approximate an expected value by some kind of Monte Carlo (MC) sampling, e.g. molecular dynamics (MD) or simulation of stochastic reaction models (also termed kinetic Monte Carlo (kMC)). Often, we are furthermore…
In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
Monte Carlo sampling techniques are used to estimate high-dimensional integrals that model the physics of light transport in virtual scenes for computer graphics applications. These methods rely on the law of large numbers to estimate…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…
We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in…
We propose sequential Monte Carlo (SMC) methods for sampling the posterior distribution of state-space models under highly informative observation regimes, a situation in which standard SMC methods can perform poorly. A special case is…
Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics…
A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…