Related papers: Multilevel Monte Carlo methods for applications in…
Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it…
Metamodels, or the regression analysis of Monte Carlo simulation results, provide a powerful tool to summarize simulation findings. However, an underutilized approach is the multilevel metamodel (MLMM) that accounts for the dependent data…
In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous…
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…
A new Monte Carlo algorithm for phase-space sampling, named (MC)**3, is presented. It is based on Markov Chain Monte Carlo techniques but at the same time incorporates prior knowledge about the target distribution in the form of suitable…
We consider several issues related to the multidimensional integration using a network of heterogeneous computers. Based on these considerations, we develop a new general purpose scheme which can significantly reduce the time needed for…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
We review the background of the cluster algorithms in Monte Carlo simulation of statistical physics problems. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local…
We present in this paper a hybrid, Multi-Level Monte Carlo (MLMC) method for solving the neutral particle transport equation. MLMC methods, originally developed to solve parametric integration problems, work by using a cheap, low fidelity…
The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of…
The simulation of the expectation of a stochastic quantity E[Y] by Monte Carlo methods is known to be computationally expensive especially if the stochastic quantity or its approximation Y_n is expensive to simulate, e.g., the solution of a…
A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features.…
We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this method from a numerical standpoint and investigated the…