Related papers: Importance Sampling for Multiscale Diffusions
Stochastic optimization techniques are standard in variational inference algorithms. These methods estimate gradients by approximating expectations with independent Monte Carlo samples. In this paper, we explore a technique that uses…
Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012)…
This paper considers the classical problem of sampling with Monte Carlo methods a target rare event distribution defined by a score function that is very expensive to compute. We assume we can build using evaluations of the true score, an…
Adjoint methods form a class of importance sampling methods that are used to accelerate Monte Carlo (MC) simulations of transport equations. Ideally, adjoint methods allow for zero-variance MC estimators provided that the solution to an…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
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…
Diffusion models have shown promising potential for advancing Boltzmann Generators. However, two critical challenges persist: (1) inherent errors in samples due to model imperfections, and (2) the requirement of hundreds of functional…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
Importance Sampling methods are broadly used to approximate posterior distributions or some of their moments. In its standard approach, samples are drawn from a single proposal distribution and weighted properly. However, since the…
Performance-based engineering for natural hazards facilitates the design and appraisal of structures with rigorous evaluation of their uncertain structural behavior under potentially extreme stochastic loads expressed in terms of failure…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
Importance sampling (IS) is a Monte Carlo technique that relies on weighted samples, simulated from a proposal distribution, to estimate intractable integrals. The quality of the estimators improves with the number of samples. However, for…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…