Related papers: Analysis of a nonlinear importance sampling scheme…

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…

Generally ``exact'' Quantum Monte Carlo computations for the ground state of many Bosons make use of importance sampling. The importance sampling is based, either on a guiding function or on an initial variational wave function. Here we…

On-line estimation plays an important role in process control and monitoring. Obtaining a theoretical solution to the simultaneous state-parameter estimation problem for non-linear stochastic systems involves solving complex…

Even though Bayesian neural networks offer a promising framework for modeling uncertainty, active learning and incorporating prior physical knowledge, few applications of them can be found in the context of interatomic force modeling. One…

Sequential algorithms such as sequential importance sampling (SIS) and sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for models not admitting a readily available likelihood function. For approximate Bayesian…

This paper deals with the Monte-Carlo methods for evaluating expectations of functionals of solutions to McKean-Vlasov Stochastic Differential Equations (MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is approximated…

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…

Markov chain Monte Carlo methods are a powerful and commonly used family of numerical methods for sampling from complex probability distributions. As applications of these methods increase in size and complexity, the need for efficient…

Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ…

The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used…

This article investigates the integration of quasi-Monte Carlo (QMC) methods using the Adaptive Multiple Importance Sampling (AMIS). Traditional Importance Sampling (IS) often suffers from poor performance since it heavily relies on the…

Sequential Monte Carlo (SMC) methods comprise one of the most successful approaches to approximate Bayesian filtering. However, SMC without good proposal distributions struggle in high dimensions. We propose nested sequential Monte Carlo…

We explore efficient estimation of statistical quantities, particularly rare event probabilities, for stochastic reaction networks. Consequently, we propose an importance sampling (IS) approach to improve the Monte Carlo (MC) estimator…

Importance sampling is a Monte Carlo method which designs estimators of expectations under a target distribution using weighted samples from a proposal distribution. When the target distribution is complex, such as multimodal distributions…

This study analyzes the nonasymptotic convergence behavior of the quasi-Monte Carlo (QMC) method with applications to linear elliptic partial differential equations (PDEs) with lognormal coefficients. Building upon the error analysis…

Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly:…

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space…