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In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…
Adaptive Monte Carlo methods are very efficient techniques designed to tune simulation estimators on-line. In this work, we present an alternative to stochastic approximation to tune the optimal change of measure in the context of…
Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
Current prevailing designs of quantum random number generators (QRNGs) designs typically employ post-processing techniques to distill raw random data, followed by statistical verification with suites like NIST SP 800-22. This paper…
We introduce the Romu family of pseudo-random number generators (PRNGs) which combines the nonlinear operation of rotation with the linear operations of multiplication and (optionally) addition. Compared to conventional linear-only PRNGs,…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…
Neutron noise in nuclear power reactors refers to the small fluctuations around the average neutron flux at steady state resulting from time-dependent perturbations inside the core. The neutron noise equations in the frequency domain can be…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
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 address the problem of detecting deviations of binary sequence from randomness,which is very important for random number (RNG) and pseudorandom number generators (PRNG). Namely, we consider a null hypothesis $H_0$ that a given bit…
The security of electronic devices has become a key requisite for the rapidly-expanding pervasive and hyper-connected world. Robust security protocols ensuring secure communication, device's resilience to attacks, authentication control and…
The ever-increasing need for random numbers is clear in many areas of computer science, from neural networks to optimization. As such, most common programming language provide easy access to Pseudorandom Number Generators. However, these…
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 discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary…
The Pseudo-Random Number Generators (PRNGs) are key tools in Monte Carlo simulations. More recently, the MIXMAX PRNG has been included in ROOT and Class Library for High Energy Physics (CLHEP) software packages and claims to be a state of…
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo…