Related papers: Unbiased Monte Carlo Simulation of Diffusion Proce…
Computing the variance of a conditional expectation has often been of importance in uncertainty quantification. Sun et al. has introduced an unbiased nested Monte Carlo estimator, which they call $1\frac{1}{2}$-level simulation since the…
We use kinetic Monte Carlo simulations to investigate current fluctuations in boundary driven generalized exclusion processes, in different dimensions. Simulation results are in full agreement with predictions based on the additivity…
In molecular simulations, efficient methods for investigating equilibration and slow relaxation in dense systems are crucial yet challenging. This study focuses on the diffusional characteristics of monodisperse hard disk systems at…
We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications…
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting…
The hardcore-Bose-Hubbard model with random chemical potential is investigated using quantum Monte Carlo simulation. We consider two cases of random distribution of the chemical potential: a uniformly random distribution and a correlated…
We propose an unbiased Monte-Carlo estimator for $\mathbb{E}[g(X_{t_1}, \cdots, X_{t_n})]$, where $X$ is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Random-walk Monte Carlo simulations are widely used to predict the optical properties of complex, disordered materials. In presence of large heterogeneities (e.g., spatially-extended nonscattering regions in a turbid environment), an…
There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
We present an overview of the variational and diffusion quantum Monte Carlo methods as implemented in the CASINO program. We particularly focus on developments made in the last decade, describing state-of-the-art quantum Monte Carlo…
In this paper, we prove a result of equivalence in law between a diffusion conditioned with respect to partial observations and an auxiliary process. By partial observations we mean coordinates (or linear transformation) of the process at a…
In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the…
We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's…
We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained.…
In statistical modeling of computer experiments sometimes prior information is available about the underlying function. For example, the physical system simulated by the computer code may be known to be monotone with respect to some or all…
Computer simulations of photon transport through an absorbing and/or scattering medium form an important research tool in astrophysics. Nearly all software codes performing such simulations for three-dimensional geometries employ the Monte…
We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase…