Related papers: Monte Carlo Simulation Techniques
Although histogram methods have been extremely effective for analyzing data from Monte Carlo simulations, they do have certain limitations, including the range over which they are valid and the difficulties of combining data from…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
A technique for reducing the number of integrals in a Monte Carlo calculation is introduced. For integrations relying on classical or mean-field trajectories with local weighting functions, it is possible to integrate analytically at least…
We apply the Direct Simulation Monte Carlo (DSMC) method, developed originally to calculate rarefied gas dynamical problems, to study the gas flow in an accretion disc in a close binary system. The method involves viscosity and thermal…
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo…
Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Radiative processes such as synchrotron radiation and Compton scattering play an important role in astrophysics. Radiative processes are fundamentally stochastic in nature, and the best tools currently used for resolving these processes…
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It relies on the explicit representation of the integrals for step functions and can…
The sampling importance resampling method is widely utilized in various fields, such as numerical integration and statistical simulation. In this paper, two modified methods are presented by incorporating two variance reduction techniques…
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…
Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…
The order of convergence of the Monte Carlo method is 1/2 which means that we need quadruple samples to decrease the error in half in the numerical simulation. Multilevel Monte Carlo methods reach the same order of error by spending less…
Indirect imaging problems in biomedical optics generally require repeated evaluation of forward models of radiative transport, for which Monte Carlo is accurate yet computationally costly. We develop a novel approach to reduce this…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…