Showing papers on "Monte Carlo method published in 2014"
Proceedings Article•
02 Apr 2014TL;DR: This paper presents a "black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation, based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the Variational distribution.
Abstract: Variational inference has become a widely used method to approximate posteriors in complex latent variables models. However, deriving a variational inference algorithm generally requires signicant model-specic analysis. These eorts can hinder and deter us from quickly developing and exploring a variety of models for a problem at hand. In this paper, we present a \black box" variational inference algorithm, one that can be quickly applied to many models with little additional derivation. Our method is based on a stochastic optimization of the variational objective where the noisy gradient is computed from Monte Carlo samples from the variational distribution. We develop a number of methods to reduce the variance of the gradient, always maintaining the criterion that we want to avoid dicult model-based derivations. We evaluate our method against the corresponding black box sampling based methods. We nd that our method reaches better predictive likelihoods much faster than sampling methods. Finally, we demonstrate that Black Box Variational Inference lets us easily explore a wide space of models by quickly constructing and evaluating several models of longitudinal healthcare data.
580 citations
TL;DR: In this paper, a new scaling model based on analytical approximations to modeled fluxes of the main atmospheric cosmic-ray particles responsible for in situ cosmogenic nuclide production is proposed.
541 citations
TL;DR: The reasons why the Monte Carlo method has evolved from a ‘last resort’ solution to a leading methodology that permeates much of contemporary science, finance, and engineering are explored.
Abstract: Since the beginning of electronic computing, people have been interested in carrying out random experiments on a computer. Such Monte Carlo techniques are now an essential ingredient in many quantitative investigations. Why is the Monte Carlo method MCM so important today? This article explores the reasons why the MCM has evolved from a 'last resort' solution to a leading methodology that permeates much of contemporary science, finance, and engineering. WIREs Comput Stat 2014, 6:386-392. doi: 10.1002/wics.1314
481 citations
TL;DR: The Monte Carlo algorithm includes quantum corrections to the photon emission, which it is shown must be included if the pair production rate is to be correctly determined.
355 citations
Posted Content•
TL;DR: This work establishes non‐asymptotic bounds for the error of approximating the target distribution by the distribution obtained by the Langevin Monte Carlo method and its variants and illustrates the effectiveness of the established guarantees.
Abstract: Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, there is no well-developed theory providing meaningful nonasymptotic guarantees for the approximate sampling procedures, especially in the high-dimensional problems. This paper makes some progress in this direction by considering the problem of sampling from a distribution having a smooth and log-concave density defined on \(\RR^p\), for some integer \(p>0\). We establish nonasymptotic bounds for the error of approximating the target distribution by the one obtained by the Langevin Monte Carlo method and its variants. We illustrate the effectiveness of the established guarantees with various experiments. Underlying our analysis are insights from the theory of continuous-time diffusion processes, which may be of interest beyond the framework of log-concave densities considered in the present work.
304 citations
TL;DR: Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave Cellular networks, in terms of coverage probability and average rate.
Abstract: In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, both in terms of coverage probability and average rate.
303 citations
Book•
28 Jan 2014
TL;DR: A robust approach to mathematical modelling and numerical simulation of multi-agent systems is presented in detail and is a useful reference text for applied mathematicians, physicists, biologists and economists who want to learn about modelling and approximation of such challenging phenomena.
Abstract: PART I: KINETIC MODELLING AND SIMULATION 1. A short introduction to kinetic equations 2. Mathematical tools 3. Monte Carlo strategies 4. Monte Carlo methods for kinetic equations PART II: MULTIAGENT KINETIC EQUATIONS 5. Models for wealth distribution 6. Opinion modelling and consensus formation 7. A further insight into economy and social sciences 8. Modelling in life sciences Appendix A: Basic arguments on Fourier transforms Appendix B: Important probability distributions
274 citations
TL;DR: Practical effect size measures and power curves that can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters are provided.
Abstract: Selecting the number of different classes which will be assumed to exist in the population is an important step in latent class analysis (LCA). The bootstrap likelihood ratio test (BLRT) provides a data-driven way to evaluate the relative adequacy of a (K -1)-class model compared to a K-class model. However, very little is known about how to predict the power or the required sample size for the BLRT in LCA. Based on extensive Monte Carlo simulations, we provide practical effect size measures and power curves which can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters. Estimated power curves and tables provide guidance for researchers wishing to size a study to have sufficient power to detect hypothesized underlying latent classes.
270 citations
01 Jan 2014
TL;DR: In this article, a Monte Carlo simulation is used to evaluate the physical quantities related to the interaction of electrons with a solid target, and the cross-sections and mean free paths have to be previously accurately calculated: they are then used in the Monte Carlo code in order to obtain the macroscopic characteristics of the interaction processes.
Abstract: Monte Carlo is one of the most powerful theoretical methods for evaluating the physical quantities related to the interaction of electrons with a solid target. A Monte Carlo simulation can be considered as an idealized experiment. The simulation does not investigate the fundamental principles of the interaction. It is necessary to have a good knowledge of them – in particular of the energy loss and angular deflection phenomena – to produce a good simulation. All the cross-sections and mean free paths have to be previously accurately calculated: they are then used in the Monte Carlo code in order to obtain the macroscopic characteristics of the interaction processes by simulating a large number of single particle trajectories and then averaging them. Due to the recent evolution in computer calculation capability, we are now able to obtain statistically significant results in very short calculation times.
268 citations
TL;DR: An overview of the use of Monte Carlo sampling-based methods for stochastic optimization problems with sampling is given, with the goal of introducing the topic to students and researchers and providing a practical guide for someone who needs to solve a stochastically optimization problem with sampling.
256 citations
TL;DR: An efficient algorithm for the inference of stochastic block models in large networks, capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster.
Abstract: We present an efficient algorithm for the inference of stochastic block models in large networks. The algorithm can be used as an optimized Markov chain Monte Carlo (MCMC) method, with a fast mixing time and a much reduced susceptibility to getting trapped in metastable states, or as a greedy agglomerative heuristic, with an almost linear O(Nln2N) complexity, where N is the number of nodes in the network, independent of the number of blocks being inferred. We show that the heuristic is capable of delivering results which are indistinguishable from the more exact and numerically expensive MCMC method in many artificial and empirical networks, despite being much faster. The method is entirely unbiased towards any specific mixing pattern, and in particular it does not favor assortative community structures.
TL;DR: In this paper, the authors introduce a variational approach for the sampling of free energy surfaces, where the bias that minimizes the functional of the bias potential relates in a simple way to the free energy surface.
Abstract: The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks A large number of solutions have been proposed to alleviate this problem Many are based on the introduction of a bias potential which is a function of a small number of collective variables However constructing such a bias is not simple Here we introduce a functional of the bias potential and an associated variational principle The bias that minimizes the functional relates in a simple way to the free energy surface This variational principle can be turned into a practical, efficient, and flexible sampling method A number of numerical examples are presented which include the determination of a three-dimensional free energy surface We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem
TL;DR: In this article, the authors apply power counting for discriminating boosted Z bosons from massive QCD jets using observables formed from the n-point energy correlation functions, and show that power counting alone gives a definite prediction for the observable that optimally separates the background-rich from the signal-rich regions of phase space.
Abstract: Optimized jet substructure observables for identifying boosted topologies will play an essential role in maximizing the physics reach of the Large Hadron Collider. Ideally, the design of discriminating variables would be informed by analytic calculations in perturbative QCD. Unfortunately, explicit calculations are often not feasible due to the complexity of the observables used for discrimination, and so many validation studies rely heavily, and solely, on Monte Carlo. In this paper we show how methods based on the parametric power counting of the dynamics of QCD, familiar from effective theory analyses, can be used to design, understand, and make robust predictions for the behavior of jet substructure variables. As a concrete example, we apply power counting for discriminating boosted Z bosons from massive QCD jets using observables formed from the n-point energy correlation functions. We show that power counting alone gives a definite prediction for the observable that optimally separates the background-rich from the signal-rich regions of phase space. Power counting can also be used to understand effects of phase space cuts and the effect of contamination from pile-up, which we discuss. As these arguments rely only on the parametric scaling of QCD, the predictions from power counting must be reproduced by any Monte Carlo, which we verify using Pythia 8 and Herwig++. We also use the example of quark versus gluon discrimination to demonstrate the limits of the power counting technique.
TL;DR: This work describes a novel nonparametric regression-based method for estimating partial EVPI that requires only the probabilistic sensitivity analysis sample and is applicable in a model of any complexity and with any specification of input parameter distribution.
Abstract: The partial expected value of perfect information (EVPI) quantifies the expected benefit of learning the values of uncertain parameters in a decision model. Partial EVPI is commonly estimated via a 2-level Monte Carlo procedure in which parameters of interest are sampled in an outer loop, and then conditional on these, the remaining parameters are sampled in an inner loop. This is computationally demanding and may be difficult if correlation between input parameters results in conditional distributions that are hard to sample from. We describe a novel nonparametric regression-based method for estimating partial EVPI that requires only the probabilistic sensitivity analysis sample (i.e., the set of samples drawn from the joint distribution of the parameters and the corresponding net benefits). The method is applicable in a model of any complexity and with any specification of input parameter distribution. We describe the implementation of the method via 2 nonparametric regression modeling approaches, the Generalized Additive Model and the Gaussian process. We demonstrate in 2 case studies the superior efficiency of the regression method over the 2-level Monte Carlo method. R code is made available to implement the method.
TL;DR: The modification allows overcoming an important limitation of the original AK-IS in that it provides the algorithm with the flexibility to deal with multiple failure regions characterized by complex, non-linear limit states.
TL;DR: Using density functional theory combined with Monte Carlo simulations, it is shown that the two dimensional MnS2 and MnSe2 sheets are ideal magnetic semiconductors with long-range magnetic ordering and high magnetic moments.
Abstract: Using density functional theory combined with Monte Carlo (MC) simulations, we show that the two dimensional (2D) MnS2 and MnSe2 sheets are ideal magnetic semiconductors with long-range magnetic ordering and high magnetic moments (3 μB per unit cell), where all the Mn atoms are ferromagnetically coupled, and the Curie temperatures (TC) estimated for MnS2 and MnSe2 by the MC simulations are 225 and 250 K, respectively, which can be further increased to 330 K and 375 K by applying 5% biaxial tensile strains.
TL;DR: In this article, the authors present a collection of local models, termed geographically weighted (GW) models, which can be found within the GWmodel R package, which uses a moving window weighting technique.
Abstract: In this study, we present a collection of local models, termed geographically weighted (GW) models, which can be found within the GWmodel R package. A GW model suits situations when spatial data are poorly described by the global form, and for some regions the localized fit provides a better description. The approach uses a moving window weighting technique, where a collection of local models are estimated at target locations. Commonly, model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed. In particular, we present case studies using: (i) GW summary statistics and a GW principal components analysis; (ii) advanced GW regression fits and diagnostics; (iii) associated Monte Carlo significance tests for non-stationarity; (iv) a GW discriminant analysis; and (v) enhanced kernel bandwidth selection procedures. General Election data-sets from the Republic of Ireland and US are used for demonstration. This study is designed to complement a companion GWmod...
TL;DR: This work proposes a new and simple routine to estimate the average experimental localization precision in SMLM, based on the nearest neighbor analysis, and shows that this approach can be generally used for any 2D or 3D S MLM data and that reliable values for the localization precision σSMLM are obtained.
Abstract: The localization precision is a crucial and important parameter for single-molecule localization microscopy (SMLM) and directly influences the achievable spatial resolution. It primarily depends on experimental imaging conditions and the registration potency of the algorithm used. We propose a new and simple routine to estimate the average experimental localization precision in SMLM, based on the nearest neighbor analysis. By exploring different experimental and simulated targets, we show that this approach can be generally used for any 2D or 3D SMLM data and that reliable values for the localization precision σ SMLM are obtained. Knowing σ SMLM is a prerequisite for consistent visualization or any quantitative structural analysis, e.g., cluster analysis or colocalization studies.
11 Nov 2014-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, generalizations of the Crystal Ball function are presented to describe mass peaks in which the per event mass resolution is unknown and marginalized over, and tested using a series of toy Monte Carlo samples generated with Pythia and smeared with different amounts of multiple scattering and for different detector resolutions.
Abstract: We present generalizations of the Crystal Ball function to describe mass peaks in which the per event mass resolution is unknown and marginalized over. The presented probability density functions are tested using a series of toy Monte Carlo samples generated with Pythia and smeared with different amounts of multiple scattering and for different detector resolutions. (C) 2014 Elsevier B.V. All rights reserved.
TL;DR: In this paper, the authors considered the estimation of Kumbhakar et al. (KLH) four random components stochastic frontier (SF) model using MLE techniques and derived the log-likelihood function of the model using results from the closed-skew normal distribution.
Abstract: This paper considers the estimation of Kumbhakar et al. (J Prod Anal. doi:
10.1007/s11123-012-0303-1
, 2012) (KLH) four random components stochastic frontier (SF) model using MLE techniques. We derive the log-likelihood function of the model using results from the closed-skew normal distribution. Our Monte Carlo analysis shows that MLE is more efficient and less biased than the multi-step KLH estimator. Moreover, we obtain closed-form expressions for the posterior expected values of the random effects, used to estimate short-run and long-run (in)efficiency as well as random-firm effects. The model is general enough to nest most of the currently used panel SF models; hence, its appropriateness can be tested. This is exemplified by analyzing empirical results from three different applications.
06 Jun 2014
TL;DR: The DELPHES C++ fast-simulation framework as discussed by the authors is a C++ framework for the simulation of a multipurpose detector response, which includes a track propagation system embedded in a magnetic field, electromagnetic and hadronic calorimeters, and a muon system.
Abstract: The new version of the DELPHES C++ fast-simulation framework is presented. The tool is written in C++ and is interfaced with the most common Monte Carlo file formats (LHEF, HepMC, STDHEP). Its purpose is the simulation of a multipurpose detector response, which includes a track propagation system embedded in a magnetic field, electromagnetic and hadronic calorimeters, and a muon system. The new modular version allows to easily produce the collections that are needed for later analysis, from low level objects such as tracks and calorimeter deposits up to high level collections such as isolated electrons, jets, taus, and missing energy.
TL;DR: It was concluded that for small sample sets the Student's t-test based on the standard error of regression models must be used and special attention must be paid on the equality of the models variances.
Posted Content•
TL;DR: Particle Markov chain Monte Carlo (PMCMC) as discussed by the authors is a systematic way of combining the two main tools used for Monte Carlo statistical inference: SMC and MCMC.
Abstract: Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a novel PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.
Book•
02 Oct 2014
TL;DR: In this paper, a short discussion of the Discrepancy Bounds is given, together with a discussion of Monte Carlo and quasi-Monte Carlo simulation for (t, m, s)-nets.
Abstract: Preface.- Notation.- 1 Introduction.- 2 Uniform Distribution Modulo One.- 3 QMC Integration in Reproducing Kernel Hilbert Spaces.- 4 Lattice Point Sets.- 5 (t, m, s)-nets and (t, s)-Sequences.- 6 A Short Discussion of the Discrepancy Bounds.- 7 Foundations of Financial Mathematics.- 8 Monte Carlo and Quasi-Monte Carlo Simulation.- Bibliography.- Index.
TL;DR: A Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof is presented.
Abstract: We present a Hamiltonian Monte Carlo algorithm to sample from multivariate Gaussian distributions in which the target space is constrained by linear and quadratic inequalities or products thereof. The Hamiltonian equations of motion can be integrated exactly and there are no parameters to tune. The algorithm mixes faster and is more efficient than Gibbs sampling. The runtime depends on the number and shape of the constraints but the algorithm is highly parallelizable. In many cases, we can exploit special structure in the covariance matrices of the untruncated Gaussian to further speed up the runtime. A simple extension of the algorithm permits sampling from distributions whose log-density is piecewise quadratic, as in the “Bayesian Lasso” model.
TL;DR: PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate, for instance, the typically high-dimensional and highly autocorrelated state trajectory in a state-space model.
Abstract: Particle Markov chain Monte Carlo (PMCMC) is a systematic way of combining the two main tools used for Monte Carlo statistical inference: sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). We present a new PMCMC algorithm that we refer to as particle Gibbs with ancestor sampling (PGAS). PGAS provides the data analyst with an off-the-shelf class of Markov kernels that can be used to simulate, for instance, the typically high-dimensional and highly autocorrelated state trajectory in a state-space model. The ancestor sampling procedure enables fast mixing of the PGAS kernel even when using seemingly few particles in the underlying SMC sampler. This is important as it can significantly reduce the computational burden that is typically associated with using SMC. PGAS is conceptually similar to the existing PG with backward simulation (PGBS) procedure. Instead of using separate forward and backward sweeps as in PGBS, however, we achieve the same effect in a single forward sweep. This makes PGAS well suited for addressing inference problems not only in state-space models, but also in models with more complex dependencies, such as non-Markovian, Bayesian nonparametric, and general probabilistic graphical models.
TL;DR: In this paper, the authors argue that Hampel's classical notion of qualitative robustness is not suitable for risk measurement, and propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz spaces.
Abstract: When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel’s classical notion of qualitative robustness is not suitable for risk measurement, and we propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz spaces. This concept captures the tradeoff between robustness and sensitivity and can be quantified by an index of qualitative robustness. By means of this index, we can compare various risk measures, such as distortion risk measures, in regard to their degree of robustness. Our analysis also yields results of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for ψ-weak convergence.
TL;DR: In this article, the authors explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations.
Abstract: In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope-based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under-recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of...
TL;DR: This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion, including Markov Chain Monte Carlo methods, the random matrices approach and Random Finite Set Statistics methods.
TL;DR: An empirical investigation is made of binary knowledge items administered in two separate surveys of a set of countries and a Monte Carlo study is presented that shows how the quality of the alignment method can be assessed.
Abstract: Asparouhov and Muthen (forthcoming) presented a new method for multiple-group confirmatory factor analysis (CFA), referred to as the alignment method. The alignment method can be used to estimate group-specific factor means and variances without requiring exact measurement invariance. A strength of the method is the ability to conveniently estimate models for many groups, such as with comparisons of countries. This paper focuses on IRT applications of the alignment method. An empirical investigation is made of binary knowledge items administered in two separate surveys of a set of countries. A Monte Carlo study is presented that shows how the quality of the alignment can be assessed.