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Monte Carlo method

About: Monte Carlo method is a research topic. Over the lifetime, 95966 publications have been published within this topic receiving 2181896 citations. The topic is also known as: MC method & Monte Carlo experiments.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, an exact method is presented for numerically calculating, within the framework of the stochastic formulation of chemical kinetics, the time evolution of any spatially homogeneous mixture of molecular species which interreact through a specified set of coupled chemical reaction channels.

5,875 citations

Journal ArticleDOI
TL;DR: In this paper, the authors describe the use of arbitrary sampling distributions chosen to facilitate the estimate of the free energy difference between a model system and some reference system, but the conventional Monte Carlo methods of obtaining such averages are inadequate for the free-energy case.

5,058 citations

Journal ArticleDOI
TL;DR: An overview of methods for sequential simulation from posterior distributions for discrete time dynamic models that are typically nonlinear and non-Gaussian, and how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literature are shown.
Abstract: In this article, we present an overview of methods for sequential simulation from posterior distributions. These methods are of particular interest in Bayesian filtering for discrete time dynamic models that are typically nonlinear and non-Gaussian. A general importance sampling framework is developed that unifies many of the methods which have been proposed over the last few decades in several different scientific disciplines. Novel extensions to the existing methods are also proposed. We show in particular how to incorporate local linearisation methods similar to those which have previously been employed in the deterministic filtering literatures these lead to very effective importance distributions. Furthermore we describe a method which uses Rao-Blackwellisation in order to take advantage of the analytic structure present in some important classes of state-space models. In a final section we develop algorithms for prediction, smoothing and evaluation of the likelihood in dynamic models.

4,810 citations

Book
01 Nov 1998
TL;DR: Information theory and log-likelihood models - a basis for model selection and inference practical use of the information theoretic approach model selection uncertainty with examples Monte Carlo insights and extended examples statistical theory.
Abstract: Information theory and log-likelihood models - a basis for model selection and inference practical use of the information theoretic approach model selection uncertainty with examples Monte Carlo insights and extended examples statistical theory.

4,340 citations

Book
04 Feb 2008
TL;DR: In this article, the authors present a method for setting up Uncertainty and Sensitivity Analyses using Monte Carlo and Linear Regression (MCF) models and a set of experiments.
Abstract: Preface. 1. Introduction to Sensitivity Analysi. 1.1 Models and Sensitivity Analysis. 1.1.1 Definition. 1.1.2 Models. 1.1.3 Models and Uncertainty. 1.1.4 How to Set Up Uncertainty and Sensitivity Analyses. 1.1.5 Implications for Model Quality. 1.2 Methods and Settings for Sensitivity Analysis - An Introduction. 1.2.1 Local versus Global. 1.2.2 A Test Model. 1.2.3 Scatterplots versus Derivatives. 1.2.4 Sigma-normalized Derivatives. 1.2.5 Monte Carlo and Linear Regression. 1.2.6 Conditional Variances - First Path. 1.2.7 Conditional Variances - Second Path. 1.2.8 Application to Model (1.3). 1.2.9 A First Setting: 'Factor Prioritization' 1.2.10 Nonadditive Models. 1.2.11 Higher-order Sensitivity Indices. 1.2.12 Total Effects. 1.2.13 A Second Setting: 'Factor Fixing'. 1.2.14 Rationale for Sensitivity Analysis. 1.2.15 Treating Sets. 1.2.16 Further Methods. 1.2.17 Elementary Effect Test. 1.2.18 Monte Carlo Filtering. 1.3 Nonindependent Input Factors. 1.4 Possible Pitfalls for a Sensitivity Analysis. 1.5 Concluding Remarks. 1.6 Exercises. 1.7 Answers. 1.8 Additional Exercises. 1.9 Solutions to Additional Exercises. 2. Experimental Designs. 2.1 Introduction. 2.2 Dependency on a Single Parameter. 2.3 Sensitivity Analysis of a Single Parameter. 2.3.1 Random Values. 2.3.2 Stratified Sampling. 2.3.3 Mean and Variance Estimates for Stratified Sampling. 2.4 Sensitivity Analysis of Multiple Parameters. 2.4.1 Linear Models. 2.4.2 One-at-a-time (OAT) Sampling. 2.4.3 Limits on the Number of Influential Parameters. 2.4.4 Fractional Factorial Sampling. 2.4.5 Latin Hypercube Sampling. 2.4.6 Multivariate Stratified Sampling. 2.4.7 Quasi-random Sampling with Low-discrepancy Sequences. 2.5 Group Sampling. 2.6 Exercises. 2.7 Exercise Solutions. 3. Elementary Effects Method. 3.1 Introduction. 3.2 The Elementary Effects Method. 3.3 The Sampling Strategy and its Optimization. 3.4 The Computation of the Sensitivity Measures. 3.5 Working with Groups. 3.6 The EE Method Step by Step. 3.7 Conclusions. 3.8 Exercises. 3.9 Solutions. 4. Variance-based Methods. 4.1 Different Tests for Different Settings. 4.2 Why Variance? 4.3 Variance-based Methods. A Brief History. 4.4 Interaction Effects. 4.5 Total Effects. 4.6 How to Compute the Sensitivity Indices. 4.7 FAST and Random Balance Designs. 4.8 Putting the Method to Work: the Infection Dynamics Model. 4.9 Caveats. 4.10 Exercises. 5. Factor Mapping and Metamodelling. 5.1 Introduction. 5.2 Monte Carlo Filtering (MCF). 5.2.1 Implementation of Monte Carlo Filtering. 5.2.2 Pros and Cons. 5.2.3 Exercises. 5.2.4 Solutions. 5.2.5 Examples. 5.3 Metamodelling and the High-Dimensional Model Representation. 5.3.1 Estimating HDMRs and Metamodels. 5.3.2 A Simple Example. 5.3.3 Another Simple Example. 5.3.4 Exercises. 5.3.5 Solutions to Exercises. 5.4 Conclusions. 6. Sensitivity Analysis: from Theory to Practice. 6.1 Example 1: a Composite Indicator. 6.1.1 Setting the Problem. 6.1.2 A Composite Indicator Measuring Countries' Performance in Environmental Sustainability. 6.1.3 Selecting the Sensitivity Analysis Method. 6.1.4 The Sensitivity Analysis Experiment and its Results. 6.1.5 Conclusions. 6.2 Example 2: Importance of Jumps in Pricing Options. 6.2.1 Setting the Problem. 6.2.2 The Heston Stochastic Volatility Model with Jumps. 6.2.3 Selecting a Suitable Sensitivity Analysis Method. 6.2.4 The Sensitivity Analysis Experiment. 6.2.5 Conclusions. 6.3 Example 3: a Chemical Reactor. 6.3.1 Setting the Problem. 6.3.2 Thermal Runaway Analysis of a Batch Reactor. 6.3.3 Selecting the Sensitivity Analysis Method. 6.3.4 The Sensitivity Analysis Experiment and its Results. 6.3.5 Conclusions. 6.4 Example 4: a Mixed Uncertainty-Sensitivity Plot. 6.4.1 In Brief. 6.5 When to use What? Afterword. Bibliography. Index.

4,306 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20242
20233,615
20227,402
20213,060
20203,230