Related papers: Monte Carlo Dynamically Weighted Importance Sampli…
This paper describes a new algorithm for Monte Carlo integration, based on the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed in detail, and its performance is evaluated in the context of Bayesian analysis, with…
Data augmentation is an effective technique to improve the generalization of deep neural networks. However, previous data augmentation methods usually treat the augmented samples equally without considering their individual impacts on the…
SEMMS (Scalable Empirical-Bayes Model for Marker Selection) is a variable-selection procedure for generalized linear models that uses a three-component normal mixture prior on regression coefficients. In its original form, SEMMS assumes…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
Importance sampling (IS) is a powerful Monte Carlo methodology for the approximation of intractable integrals, very often involving a target probability density function. The performance of IS heavily depends on the appropriate selection of…
A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…
Modern optimizers such as AdamW, equipped with momentum and adaptive learning rate, are designed to escape local minima and explore the vast parameter space. This exploration is beneficial for finding good loss basins when training from…
We present a general sample reweighting scheme and its underlying theory for the integration of an unknown function with low dimensionality. Our method produces better results than standard weighting schemes for common sampling strategies,…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps…
Efficiently sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference for astrophysics, especially gravitational-wave astronomy. Popular families of methods like Markov-chain Monte Carlo, nested…
Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…
Importance sampling and independent Metropolis-Hastings (IMH) are among the fundamental building blocks of Monte Carlo methods. Both require a proposal distribution that globally approximates the target distribution. The Radon-Nikodym…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
We revisit the theory of importance weighted variational inference (IWVI), a promising strategy for learning latent variable models. IWVI uses new variational bounds, known as Monte Carlo objectives (MCOs), obtained by replacing intractable…
This paper presents two novel ensemble domain decomposition methods for fast-solving the Stokes-Darcy coupled models with random hydraulic conductivity and body force. To address such random systems, we employ the Monte Carlo (MC) method to…
Distributed detection fusion with high-dimension conditionally dependent observations is known to be a challenging problem. When a fusion rule is fixed, this paper attempts to make progress on this problem for the large sensor networks by…
We propose and analyze an adaptive finite element method for a phase-field model of dynamic brittle fracture. The model couples a second-order hyperbolic equation for elastodynamics with the Ambrosio-Tortorelli regularization of the…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
Numerous studies have focused on learning and understanding the dynamics of physical systems from video data, such as spatial intelligence. Artificial intelligence requires quantitative assessments of the uncertainty of the model to ensure…