Related papers: Importance Gaussian Quadrature
Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted…
The effective sample size (ESS) measures the informational value of a probability distribution in terms of an equivalent number of study participants. The ESS plays a crucial role in estimating the Expected Value of Sample Information…
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many…
We develop a theoretical framework for studying numerical estimation of lower previsions, generally applicable to two-level Monte Carlo methods, importance sampling methods, and a wide range of other sampling methods one might devise. We…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
The Auto-Importance Sampling (AIS) method is a Monte Carlo variance reduction technique proposed for deep penetration problems, which can significantly improve computational efficiency without pre-calculations for importance distribution.…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution given its unnormalized density function. This algorithm relies on a sequence of interpolating distributions bridging the target to an initial…
This paper introduces a sequential multiple importance sampling (SeMIS) algorithm for high-dimensional Bayesian inference. The method estimates Bayesian evidence using all generated samples from each proposal distribution while obtaining…
One of the well-known challenges in optimal experimental design is how to efficiently estimate the nested integrations of the expected information gain. The Gaussian approximation and associated importance sampling have been shown to be…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
Ab initio nuclear many-body frameworks require extensive computational resources, especially when targeting heavier nuclei. Importance-truncation (IT) techniques allow to significantly reduce the dimensionality of the problem by neglecting…
Numerical integration and emulation are fundamental topics across scientific fields. We propose novel adaptive quadrature schemes based on an active learning procedure. We consider an interpolative approach for building a surrogate…
The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric…
In this paper, we propose a novel and generic family of multiple importance sampling estimators. We first revisit the celebrated balance heuristic estimator, a widely used Monte Carlo technique for the approximation of intractable…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…