Related papers: Monte Carlo Methods in Statistics
Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with…
Least squares Monte Carlo methods are a popular numerical approximation method for solving stochastic control problems. Based on dynamic programming, their key feature is the approximation of the conditional expectation of future rewards by…
This article reviews the basic computational techniques for carrying out multi-scale simulations using statistical methods, with the focus on simulations of epitaxial growth. First, the statistical-physics background behind Monte Carlo…
While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error.…
In 1946, S. Ulam invented Monte Carlo method, which has since become the standard numerical technique for making statistical predictions for long-term behaviour of dynamical systems. We show that this, or in fact any other numerical…
I show how to construct Monte Carlo algorithms (programs), prove that they are correct and document them. Complicated algorithms are build using a handful of elementary methods. This construction process is transparently illustrated using…
Monte Carlo simulation is an essential component of experimental particle physics in all the phases of its life-cycle: the investigation of the physics reach of detector concepts, the design of facilities and detectors, the development and…
Identification of nonlinear systems is a challenging problem. Physical knowledge of the system can be used in the identification process to significantly improve the predictive performance by restricting the space of possible mappings from…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
Since the middle of the 1940's scientists have used Monte Carlo (MC) simulations to obtain information about physical processes. This has proved a accurate and and reliable method to obtain this information. Through out resent years…
These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques…
The Self-Learning Monte Carlo (SLMC) method is a Monte Carlo approach that has emerged in recent years by integrating concepts from machine learning with conventional Monte Carlo techniques. Designed to accelerate the numerical study of…
The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in…
The underlying physics of basketball shooting seems to be a straightforward example of the Newtonian mechanics that can easily be traced by numerical methods. However, a human basketball player does not make use of all the possible…
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.…
We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the…
The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad…
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…