Home About us Contact
|
Home About us Contact | ||
|
|
||
Simulation Error (simulation + error)
Selected AbstractsA theory of statistical models for Monte Carlo integrationJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2003A. Kong Summary. The task of estimating an integral by Monte Carlo methods is formulated as a statistical model using simulated observations as data. The difficulty in this exercise is that we ordinarily have at our disposal all of the information required to compute integrals exactly by calculus or numerical integration, but we choose to ignore some of the information for simplicity or computational feasibility. Our proposal is to use a semiparametric statistical model that makes explicit what information is ignored and what information is retained. The parameter space in this model is a set of measures on the sample space, which is ordinarily an infinite dimensional object. None-the-less, from simulated data the base-line measure can be estimated by maximum likelihood, and the required integrals computed by a simple formula previously derived by Vardi and by Lindsay in a closely related model for biased sampling. The same formula was also suggested by Geyer and by Meng and Wong using entirely different arguments. By contrast with Geyer's retrospective likelihood, a correct estimate of simulation error is available directly from the Fisher information. The principal advantage of the semiparametric model is that variance reduction techniques are associated with submodels in which the maximum likelihood estimator in the submodel may have substantially smaller variance than the traditional estimator. The method is applicable to Markov chain and more general Monte Carlo sampling schemes with multiple samplers. [source] Importance of interpolation when constructing double-bootstrap confidence intervalsJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2000Peter Hall We show that, in the context of double-bootstrap confidence intervals, linear interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Intervals that are indistinguishable in terms of coverage error with theoretical, infinite simulation, double-bootstrap confidence intervals may be obtained at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of uniform bootstrap sampling and require no special analysis or computational techniques. Interpolation at the first level of the double bootstrap is shown to have a relatively minor effect on the simulation error. [source] SIMULATED MAXIMUM LIKELIHOOD APPLIED TO NON-GAUSSIAN AND NONLINEAR MIXED EFFECTS AND STATE,SPACE MODELSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 4 2004Russell B. Millar Summary The paper presents an overview of maximum likelihood estimation using simulated likelihood, including the use of antithetic variables and evaluation of the simulation error of the resulting estimates. It gives a general purpose implementation of simulated maximum likelihood and uses it to re-visit four models that have previously appeared in the published literature: a state,space model for count data; a nested random effects model for binomial data; a nonlinear growth model with crossed random effects; and a crossed random effects model for binary salamander-mating data. In the case of the last three examples, this appears to be the first time that maximum likelihood fits of these models have been presented. [source] Error-correction methods and evaluation of an ensemble based hydrological forecasting system for the Upper Danube catchmentATMOSPHERIC SCIENCE LETTERS, Issue 2 2008K. Bogner Abstract Within the EU Project PREVention, Information and Early Warning (PREVIEW), ensembles of discharge series have been generated for the Danube catchment by the use of various weather forecast products. Hydrological models applied for streamflow prediction often have simulation errors that degrade forecast quality and limit the operational usefulness of the forecasts. Therefore, error-correction methods have been tested for adjusting the ensemble traces using a transformation derived with simulated and observed flows. This article presents first results of the combination of state-space models and wavelet transformations in order to update errors between the simulated (forecasted) and the observed discharge. Copyright © 2008 Royal Meteorological Society [source] | ||||||||||