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Monte Carlo Error Analysis

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Monte Carlo Error Definition

a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: Sign up Here's how it works: monte carlo error estimation Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Required number of simulations for Monte Carlo analysis up vote 7 down vote favorite My question is about the required number of simulations for Monte Carlo analysis method. As far as I see the required number of simulations for any allowed percentage error $E$ (e.g., 5) is monte carlo integration error $$ n = \left\{\frac{100 \cdot z_c \cdot \text{std}(x)}{E \cdot \text{mean}(x)} \right\}^2 , $$ where $\text{std}(x)$ is the standard deviation of the resulting sampling, and $z_c$ is the confidence level coefficient (e.g., for 95% it is 1.96). So in this way it is possible to check that the resulting mean and standard deviation of $n$ simulations represent actual mean and standard deviation with 95% confidence level. In my case I run the simualtion 7500 times, and compute moving means and standard deviations for each set of 100 sampling out of the 7500 simulations. The required number of simulation I obtain is always less than 100, but % error of mean and std compare to mean and std of entire results is not always less than 5%. In most cases the % error of mean is less than 5% but the error of std goes up to 30%. What is the best way to determine number of required simulation without know actual mean and std (in my case subjected outcome of simulation is normally distributed)? Thanks in advance for any help. In order to have an idea about what may distribution of simulation results look like when itera

or suggestions for references to include. There's no need to point out busted links (?? in LaTeX) because the computer

Monte Carlo Error Propagation

will catch those for me when it is time to root out monte carlo standard error definition the last of them. @book{mcbook,
   author = {Art B. Owen},    year = 2013,    title

Monte Carlo Error Bootstrap

= {Monte Carlo theory, methods and examples} } Copyright Art Owen, 2009-2013. Contents Introduction Simple Monte Carlo Uniform random numbers Non-uniform random numbers Random vectors and objects Processes Other http://stats.stackexchange.com/questions/95779/required-number-of-simulations-for-monte-carlo-analysis integration methods Variance reduction Importance sampling Advanced variance reduction Markov chain Monte Carlo Gibbs sampler Adaptive and accelerated MCMC Sequential Monte Carlo Quasi-Monte Carlo Lattice rules Randomized quasi-Monte Carlo Chapters 1 and 2 1 Introduction Example: traffic modeling Example: interpoint distances Notation Outline of the book End notes Exercises 2 Simple Monte Carlo Accuracy of simple Monte Carlo http://statweb.stanford.edu/~owen/mc/ Error estimation Safely computing the standard error Estimating probabilities Estimating quantiles Random sample size When Monte Carlo fails Chebychev and Hoeffding intervals End notes Exercises 3 Uniform Random Numbers Random and pseudo-random numbers States, periods, seeds, and streams U(0,1) random variables Inside a random number generator Uniformity measures Statistical tests of random numbers Pairwise independent random numbers End notes Exercises 4 Non-uniform Random Numbers Inverting the CDF Examples of inversion Inversion for the normal distribution Inversion for discrete random variables Numerical inversion Other transformations Acceptance-rejection Gamma random variables Mixtures and automatic generators End notes Exercises 5 Random vectors and objects Generalizations of one-dimensional methods Multivariate normal and t Multinomial Dirichlet Multivariate Poisson and other distributions Copula-marginal sampling Random points on the sphere Random matrices Example: classification error rates Random permutations Sampling without replacement Random graphs End notes Exercises 6 Processes Stochastic process definitions Discrete time random walks Gaussian processes Detailed simulation of Brownian motion Stochastic differential equations Non-Poisson point processes Dirichlet processes Discrete state, continuous time processes End notes Exercises 7 Other qua

Health Search databasePMCAll DatabasesAssemblyBioProjectBioSampleBioSystemsBooksClinVarCloneConserved DomainsdbGaPdbVarESTGeneGenomeGEO DataSetsGEO ProfilesGSSGTRHomoloGeneMedGenMeSHNCBI http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3337209/ Web SiteNLM CatalogNucleotideOMIMPMCPopSetProbeProteinProtein ClustersPubChem BioAssayPubChem CompoundPubChem SubstancePubMedPubMed HealthSNPSRAStructureTaxonomyToolKitToolKitAllToolKitBookToolKitBookghUniGeneSearch termSearch Advanced Journal list Help Journal ListHHS Author ManuscriptsPMC3337209 Am Stat. Author manuscript; available in PMC 2012 Apr 25.Published in final edited form as:Am Stat. 2009 May 1; 63(2): 155–162. doi:  monte carlo 10.1198/tast.2009.0030PMCID: PMC3337209NIHMSID: NIHMS272824On the Assessment of Monte Carlo Error in Simulation-Based Statistical AnalysesElizabeth Koehler, Biostatistician, Elizabeth Brown, Assistant Professor, and Sebastien J.-P. A. Haneuse, Associate Scientific InvestigatorElizabeth Koehler, Department of Biostatistics, Vanderbilt University, Nashville, TN 37232;Contributor Information.Elizabeth Koehler: ude.tlibrednav@relheok.e; monte carlo error Elizabeth Brown: ude.notgnihsaw@bazile; Sebastien J.-P. A. Haneuse: gro.chg@s.esuenah Author information ► Copyright and License information ►Copyright notice and DisclaimerSee other articles in PMC that cite the published article.AbstractStatistical experiments, more commonly referred to as Monte Carlo or simulation studies, are used to study the behavior of statistical methods and measures under controlled situations. Whereas recent computing and methodological advances have permitted increased efficiency in the simulation process, known as variance reduction, such experiments remain limited by their finite nature and hence are subject to uncertainty; when a simulation is run more than once, different results are obtained. However, virtually no emphasis has been placed on reporting the uncertainty, referred to here as Monte Carlo e

 

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