Search results for "Monte Carlo integration"
showing 10 items of 24 documents
Adaptive Population Importance Samplers: A General Perspective
2016
Importance sampling (IS) is a well-known Monte Carlo method, widely used to approximate a distribution of interest using a random measure composed of a set of weighted samples generated from another proposal density. Since the performance of the algorithm depends on the mismatch between the target and the proposal densities, a set of proposals is often iteratively adapted in order to reduce the variance of the resulting estimator. In this paper, we review several well-known adaptive population importance samplers, providing a unified common framework and classifying them according to the nature of their estimation and adaptive procedures. Furthermore, we interpret the underlying motivation …
CLUSTER MONTE CARLO ALGORITHMS IN STATISTICAL MECHANICS
1992
The cluster Monte Carlo method, where variables are updated in groups, is very efficient at second order phase transitions. Much better results can be obtained with less computer time. This article reviews the method of Swendsen and Wang and some of its applications.
Group Metropolis Sampling
2017
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized with one summary particle and one summary weight. GIS facilitates the design of novel efficient MC techniques. For instance, we present the Group Metropolis Sampling (GMS) algorithm which produces a Markov chain of sets of weighted samples. GMS in general outperforms other multiple try schemes…
Monte Carlo Simulations in Polymer Science
2012
Monte Carlo methods are useful for computing the statistical properties of both single macromolecules of various chemical architectures and systems containing many polymers (solutions, melts, blends, etc.). Starting with simple models (lattice models such as the self-avoiding walk or the bond fluctuation model, as well as coarse-grained or chemically realistic models in the continuum) various algorithms exist to generate conformations typical for thermal equilibrium, but dynamic Monte Carlo methods can also model diffusion and relaxation processes (as described by the Rouse and the reptation models for polymer melt dynamics). Limitations of the method are explained, and also the measures to…
Multi-boson block factorization of fermions
2017
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the g…
Monte carlo methods in quantum many-body theories
2008
This is an introduction of Monte Carlo methods for beginners and their application to some quantum many-body problems. Special emphasis is done on the methodology and the general characteristics of Monte Carlo calculations. An introduction to the applications to many-body physics, specifically the Variational Monte Carlo and the Green Function Monte Carlo, is also included.
Critical phenomena without “hyper scaling”: How is the finite-size scaling analysis of Monte Carlo data affected?
2010
Abstract The finite size scaling analysis of Monte Carlo data is discussed for two models for which hyperscaling is violated: (i) the random field Ising model (using a model for a colloid-polymer mixture in a random matrix as a representative) (ii) The Ising bi-pyramid in computing surface fields.
Path integral Monte Carlo study of the internal quantum state dynamics of a generic model fluid
1996
We study the quantum dynamics of a generic model fluid with internal quantum states and classical translational degrees of freedom in two spatial dimensions. The path integral Monte Carlo data for the imaginary time correlation functions are presented and analyzed by the maximum entropy method. A comparison of the frequency distribution with those of a mean field approximation and virial expansion shows good agreement at high and low densities, respectively. \textcopyright{} 1996 The American Physical Society.
Sequential Monte Carlo Methods in Random Intercept Models for Longitudinal Data
2017
Longitudinal modelling is common in the field of Biostatistical research. In some studies, it becomes mandatory to update posterior distributions based on new data in order to perform inferential process on-line. In such situations, the use of posterior distribution as the prior distribution in the new application of the Bayes’ theorem is sensible. However, the analytic form of the posterior distribution is not always available and we only have an approximated sample of it, thus making the process “not-so-easy”. Equivalent inferences could be obtained through a Bayesian inferential process based on the set that integrates the old and new data. Nevertheless, this is not always a real alterna…
Non-linear systems under parametric white noise input: digital simulation and response
2005
Abstract Monte Carlo technique is constituted of three steps. Therefore, improving such technique in practice means, improving the procedure used in one of the three following steps: (i) sample paths of the stochastic input process, (ii) calculation of the outputs corresponding to the generated input samples by using methods of classical dynamics and (iii) estimating statistics of the output process from sample outputs related to the previous step. For linear and non-linear systems driven by parametric impulsive inputs such as normal or non-normal white noises, a general integration method requires a considerable reduction of the integration step when the impulse occurs, treating the impuls…