Latin hypercube sampling in excel3/15/2024 Where "x" is the parameter value, is the parameter minimum, is the parameter maximum, and is the standard uniform value.Ĭonverting LHS output from Standard Normal to Parameter Space _ Each random sample can be converted to parameter values via the following equations:Ĭonverting LHS output from Standard Uniform to Parameter Space _ This code outputs samples for the standard uniform and standard normal distributions. Posterior Distribution – the resulting statistical distribution of the model outputĪn example implementation of a LHS algorithm is below. Prior Distribution – the statistical distribution of the input parameters to a model Due to the possibility of clustering (LHS sample with points close together) of sample points, a nearest neighbour restriction can be imposed. This is best visualized in a 2D space with the following figure:Īs seen in Figure 1, there is only one sample in each row and column in (X,Y) space. Once a suitable CDF sample is made, the sample CDF value is inversely mapped back to a parameter value.Ī requirement for LHS is that each region of the CDF can only be sampled once for each parameter. By representing each variable as its Cumulative Distribution Function (CDF) (prior distribution) and partitioning the CDF into N regions and taking a single sample from each region, this increases the likelihood that the full range of the posterior distribution is sampled. LHS typically requires less samples and converges faster than Monte Carlo Simple Random Sampling (MCSRS) methods when used in uncertainty analysis. Latin Hypercube Sampling (LHS) is a method of sampling a model input space, usually for obtaining data for training metamodels or for uncertainty analysis. 3.2 Converting LHS output from Standard Normal to Parameter Space.3.1 Converting LHS output from Standard Uniform to Parameter Space.Volkova, E., Iooss, B., Van Dorpe, F.: Global sensitivity analysis for a numerical model of radionuclide migration from the RRC “Kurchatov Institute” radwaste disposal site. Stein, M.: Large sample properties of simulations using Latin hypercube sampling. Sobol, I.: Uniformly distributed sequences with additional uniformity property. Simpson, T., Peplinski, J., Kock, P., Allen, J.: Metamodel for computer-based engineering designs: Survey and recommendations. Simpson, T., Lin, D., Chen, W.: Sampling strategies for computer experiments: Design and analysis. Wiley Series in Probability and Statistics. Pistone, G., Vicario, G.: Comparing and generating Latin Hypercube designs in Kriging models. In: Actes de MATERIAUX, Dijon, France, 2006 Petelet, M., Asserin, O., Iooss, B., Loredo, A.: Echantillonnage LHS des propriétés matériau des aciers pour l’analyse de sensibilité globale en simulation numérique du soudage. Thèse de l’Université de Bourgogne (2007) Petelet, M.: Analyse de sensibilité globale de modèles thermomécaniques de simulation numérique du soudage. Park, J.-S.: Optimal Latin-hypercube designs for computer experiments. Owen, A.: A central limit theorem for Latin hypercube sampling. McKay, M., Beckman, R., Conover, W.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Levy, S., Steinberg, D.: Computer experiments: A review. Kurowicka, D., Cooke, R.: Uncertainty Analysis with High Dimensional Dependence Modelling. Kleijnen, J.: Design and Analysis of Simulation Experiments. Jourdan, A., Franco, J.: Optimal Latin hypercube designs for the Kullback-Leibler criterion. Iooss, B., Boussouf, L., Feuillard, V., Marrel, A.: Numerical studies of the metamodel fitting and validation processes. Iman, R., Conover, W.: A distribution-free approach to inducing rank correlation among input variables. Helton, J., Davis, F.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Gentle, J.: Random Number Generation and Monte Carlo Methods. Wiley, New York (2008)įang, K.-T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. (eds.): Uncertainty in Industrial Practice. 28, 667–680 (2008)īursztyn, D., Steinberg, D.: Comparison of designs for computer experiments. Available at URL: īorgonovo, E.: Sensitivity analysis of model output with input constraints: A generalized rationale for local methods. Asserin, O., Loredo, A., Petelet, M., Iooss, B.: Global sensitivity analysis in welding simulations-What are the material data you really need? Finite Elem.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |