Related papers: Unbiased Monte Carlo Simulation of Diffusion Proce…

Estimating the unknown density from which a given independent sample originates is more difficult than estimating the mean, in the sense that for the best popular non-parametric density estimators, the mean integrated square error converges…

We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…

Monte Carlo experiments produce samples in order to estimate features of a given distribution. However, simultaneous estimation of means and quantiles has received little attention, despite being common practice. In this setting we…

Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of…

Physically-based renderings contain Monte-Carlo noise, with variance that increases as the number of rays per pixel decreases. This noise, while zero-mean for good modern renderers, can have heavy tails (most notably, for scenes containing…

Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem,…

As it follows from the interrelation of Gamma and Poisson distributions the observed value of asymmetry for Poisson flows of events has the bias. The Monte Carlo experiment confirms the presence of this bias between the observed and initial…

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

On the base of a Feynman-Kac--type formula involving Poisson stochastic processes, recently a Monte Carlo algorithm has been introduced, which describes exactly the real- or imaginary-time evolution of many-body lattice quantum systems. We…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good…

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…

We look at Monte Carlo numerical integration from a stochastic geometry point of view. While crude Monte Carlo estimators relate to linear statistics of a homogeneous Poisson point process (PPP), linear statistics of more regularly spread…

We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…

Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…

We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system in a homogeneous cooling state. The system contains an arbitrary number of species of different sizes and masses. The…

Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…

Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…

We introduce a method for non-uniform random number generation based on sampling a physical process in a controlled environment. We demonstrate one proof-of-concept implementation of the method that reduces the error of Monte Carlo…

For long term investments, model portfolios are defined at the level of indexes, a setup known as Strategic Asset Allocation (SAA). The possible outcomes at a scale of a few decades can be obtained by Monte Carlo simulations, resulting in a…