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Monte Carlo Error Analysis

available in PMC 2012 Apr 25.Published in final edited form as:Am Stat. 2009 May 1;

Monte Carlo Error Definition

63(2): 155–162. doi:  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.

Monte Carlo Integration Error

A. Haneuse, Associate Scientific InvestigatorElizabeth Koehler, Department of Biostatistics, Vanderbilt University, Nashville, TN 37232;Contributor Information.Elizabeth Koehler: ude.tlibrednav@relheok.e; 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 monte carlo standard error definition 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 error, associated with simulation results in the published literature, or on justifying the number of replications used. These deserve broader consideration. Here we present a series of simple and practical methods for estimating Monte Carlo error as well as determining the number of replications required to achieve a desired level of accuracy. The issues and methods are demonstrated with two simple examples, one evaluating operating characteristics o

Pseudo-failures to replicate » Markov chain Monte Carlo standard errors Posted byAndrew on 2 April 2007, 12:36 am Galin Jones sent me this paper (by James Flegal, Murali Haran, and himself) which he said started with a suggestion I monte carlo error propagation once made to him long ago. That's pretty cool! Here's the abstract: Current reporting monte carlo integration algorithm of results based on Markov chain Monte Carlo computations could be improved. In particular, a measure of the accuracy of the resulting monte carlo integration example estimates is rarely reported in the literature. Thus the reader has little ability to objectively assess the quality of the reported estimates. This paper is an attempt to address this issue in that we discuss https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3337209/ why Monte Carlo standard errors are important, how they can be easily calculated in Markov chain Monte Carlo and how they can be used to decide when to stop the simulation. We compare their use to a popular alternative in the context of two examples. This is a clear paper with some interesting results. My main suggestion is to distinguish two goals: estimating a parameter in a model and estimating http://andrewgelman.com/2007/04/02/markov_chain_mo/ an expectation. To use Bayesian notation, if we have simulations theta_1,…,theta_L from a posterior distribution p(theta|y), the two goals are estimating theta or estimating E(theta|y). (Assume for simplicity here that theta is a scalar, or a scalar summary of a vector parameter.) Inference for theta or inference for E(theta) When the goal is to estimate theta, then all you really need is to estimate theta to more accuracy than its standard error (in Bayesian terms, its posterior standard deviation). For example, if a parameter is estimated at 3.5 +/- 1.2, that's fine. There's no point in knowing that the posterior mean is 3.538. To put it another way, as we draw more simulations, we can estimate that "3.538" more precisely-our standard error on E(theta|y) will approach zero-but that 1.2 ain't going down much. The standard error on theta (that is, sd(theta|y)) is what it is. This is a general issue in simulation (not just using Markov chains), and we discuss it on page 277 of Bayesian Data Analysis (second edition): if the goal is inference about theta, and you have 100 or more independent simulation draws, then the Monte Carlo error adds almost nothing to the uncertainty coming from the actual posterior variance. On the other hand, if your g

Software MTK++/MCPB http://www.merzgroup.org/mc-error-estimation.html HeatMap DivCon MC Error Estimation QUICK WHAM-GPU DBs 1HSG 1UBQ BSSE Estimator Links Photos JACS Cover AMBER 12 Cover Angkor Istanbul Petra Alhambra Greece Barcelona Florence Rome Pisa monte carlo Barcelona > Parc Güell News This is an example of using Monte Carlo error propagation analysis on a simple Lennard-Jones potential energy surface as described in:Faver, J. C. monte carlo error Ucisik, M. N., Yang, W., Merz, K. M. Computer-aided Drug Design: Using Numbers to your Advantage. ACS Med. Chem. Lett. 2013, in pressFaver, J. C., Yang,W., Merz, K. M. (2012)The Effects of Computational Modeling Errors on the Estimation of Statistical Mechanical VariablesJournal of Chemical Theory and Computation 8,3769–3776. nstate.cppFile Size: 3 kbFile Type: cppDownload File Create a free website Powered by Create your own free website Start your own free website A surprisingly easy drag & drop site creator. Learn more. ✕

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