Related papers: An Introduction to Monte Carlo Simulation of Stati…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
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…
Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
A numerical technique is introduced that reduces exponentially the time required for Monte Carlo simulations of non-equilibrium systems. Results for the quasi-stationary probability distribution in two model systems are compared with the…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
Monte Carlo algorithms are a foundational pillar of modern computational science, yet their effective application hinges on a deep understanding of their performance trade offs. This paper presents a critical analysis of the evolution of…
We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the…
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…
The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis can not be based on simple Gaussian assumptions. To this extent a method is…
A classical Monte Carlo algorithm based on the quasi-classical approximation is applied to the pseudospin Hamiltonian of the model cuprate. The model takes into account both local and non-local correlations, Heisenberg spin-exchange…
We consider quantile estimation using Markov chain Monte Carlo and establish conditions under which the sampling distribution of the Monte Carlo error is approximately Normal. Further, we investigate techniques to estimate the associated…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data.…
Monte Carlo methods are now an essential part of the statistician's toolbox, to the point of being more familiar to graduate students than the measure theoretic notions upon which they are based! We recall in this note some of the advances…
I discuss optimized data analysis and Monte Carlo methods. Reweighting methods are discussed through examples, like Lee-Yang zeroes in the Ising model and the absence of deconfinement in QCD. I discuss reweighted data analysis and…