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We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution…
We apply multilevel Monte Carlo for option pricing problems using exponential L\'{e}vy models with a uniform timestep discretisation to monitor the running maximum required for lookback and barrier options. The numerical results demonstrate…
We develop a Monte-Carlo based numerical method for solving discrete-time stochastic optimal control problems with inventory. These are optimal control problems in which the control affects only a deterministically evolving inventory…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
An efficient O(N) cluster Monte Carlo method for Ising models with long-range interactions is presented. Our novel algorithm does not introduce any cutoff for interaction range and thus it strictly fulfills the detailed balance. The…
We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into…
We present a Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm for detecting hidden variables in a continuous time Bayesian network (CTBN), which uses reversible jumps in the sense defined by (Green 1995). In common with several…
We present an exact Monte Carlo algorithm designed to sample theories where the energy is a sum of many couplings of decreasing strength. The algorithm avoids the computation of almost all non-leading terms. Its use is illustrated by…
Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard…
Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method…
We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a…
We consider generalizations of the classical inverse problem to Bayesien type estimators, where the result is not one optimal parameter but an optimal probability distribution in parameter space. The practical computational tool to compute…
We present a method which extends Monte Carlo studies to situations that require a large dynamic range in particle number. The underlying idea is that, in order to calculate the collisional evolution of a system, some particle interactions…
Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…
An ultracold Fermi gas with a zero-range attractive potential in the unitary limit is investigated using variational and diffusion Monte Carlo methods. Previous calculations have used a finite range interactions and extrapolate the results…
We develop a variational Monte Carlo (VMC) method for electron-phonon coupled systems. The VMC method has been extensively used for investigating strongly correlated electrons over the last decades. However, its applications to…
We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the…
We present a population control method with sampling and regulation steps for Monte Carlo particles involved in the numerical simulation of a transport equation. We recall in the first section the difficulties related to the variance…
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of…
We consider a generalization of the standard Metropolis algorithm acceptance/rejection decision rule and numerically explore its properties using auxiliary field quantum Monte Carlo. The generalization involves a free parameter which, given…