Related papers: Efficient method of finding scaling exponents from…
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method…
This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a…
We present bounds for the finite sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties…
Monte Carlo simulation has been performed in a two-dimensional modified XY-model first proposed by Domany et. al [E. Domany, M. Schick and R. H. Swendsen, Phys. Rev. Lett. 52, 1535 (1984)]. The cluster algorithm of Wolff has been used and…
We study the feature-scaled version of the Monte Carlo algorithm with linear function approximation. This algorithm converges to a scale-invariant solution, which is not unduly affected by states having feature vectors with large norms. The…
Motivated mainly by applications to partial differential equations with random coefficients, we introduce a new class of Monte Carlo estimators, called Toeplitz Monte Carlo (TMC) estimator for approximating the integral of a multivariate…
In this work we have studied the dynamic scaling behavior of two scaling functions and we have shown that scaling functions obey the dynamic finite size scaling rules. Dynamic finite size scaling of scaling functions opens possibilities for…
The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated…
We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data…
In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such…
We describe a regression-based method, generally referred to as the Least Squares Monte Carlo (LSMC) method, to speed up exposure calculations of a portfolio. We assume that the portfolio contains several exotic derivatives that are priced…
We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…
We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo…
We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This…
We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
A method is proposed to handle the sign problem in the simulation of systems having indefinite or complex-valued measures. In general, this new approach, which is based on renormalisation blocking, is shown to yield statistical errors…
We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…