Liefvendahl, M., Stocki, R.: A study on algorithms for optimization of Latin hypercubes. In: Inference Control in Statistical Databases, Springer, pp.
In: Proceedings of the 12th International Probabilistic Workshop, Weimar (2014)ĭandekar, R.A., Cohen, M., Kirkendall, N.: Sensitive micro data protection using Latin hypercube sampling technique. Schmidt, R., Voigt, M., Vogeler, K.: Extension of Latin hypercube samples while maintaining the correlation structure. Huntington, D.E., Lyrintzis, C.S.: Improvements to and limitations of Latin hypercube sampling. Sallaberry, C., Helton, J., Hora, S.: Extension of Latin hypercube samples with correlated variables. Vořechovský, M., Novák, D.: Correlation control in small-sample Monte Carlo type simulations I: a simulated annealing approach. Vořechovský, M.: Hierarchical refinement of Latin hypercube samples. In: 4th International Workshop on Reliable Engineering Computing (2010) The package includes additional functionality for the creation of an optimised subset of an existing plan. lhsdesignmodified provides a latin hypercube sample of n values of each of p variables but unlike lhsdesign, the variables can range between any minimum and maximum number specified by the user, where as lhsdesign only provide data between 0 and 1 which might not be very helpful in many practical problems where the range is not bound to 0 and 1.
The genetic optimisation algorithm is largely based on the work by Bates et al. lhsdesignmodified is a modification of the Matlab Statistics function lhsdesign. Vořechovský, M.: Extension of sample size in Latin hypercube sampling with correlated variables. LatinHypercubeSampling is a Julia package for the creation of optimised Latin Hypercube Sampling Plans.
#MATLAB LATIN HYPERCUBE SAMPLING HOW TO#
Welcome back This is number two in a series of five blog posts that describe how to construct a Monte Carlo risk analysis application in Excel VBA. Tong, C.: Refinement strategies for stratified sampling methods. VBA Monte Carlo risk analysis spreadsheet with correlation using the Iman-Conover method. In: 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, University of Texas at San Antonio (2005) X lhsdesign (n,p,Name,Value) modifies the resulting design using one or more name-value pair arguments. For each column of X, the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n). You are not gaining any of the efficiency of the LHS design, so that is not normally how LHS algorithms are written.Pleming, J.B., Manteufel, R.D.: Replicated Latin hypercube sampling. X lhsdesign (n,p) returns a Latin hypercube sample matrix of size n -by- p. A lhsmdu program is shown that will calculate an L x N input matrix for N variables and L realizations. If you want to iterate through all possible LHS designs, you are essentially conducting an experiment at every design cell location. An extension of Latin hypercube sampling (LHSMDU) for multivariate models with limited realizations is presented which enforces multidimensional uniformity of the input parameters through sequential realization elimination. The point is that the one LHS with one arrangement of cells is a more efficient sample of the design space than a strictly simple random sample of the same design space of equivalent sample size. Any one LHS will intentionally only pick one of those arrangements. If you consider only the "cell" of the LHS as a unique sample, then there are, as you said, n!^(p-1) different arrangements of cells. X is similar to a random sample from the multivariate normal distribution, but the marginal distribution of each column is adjusted so that its sample marginal distribution is close to its theoretical normal distribution. There are an infinite number of unique samples that can be drawn since the samples are stratified simple random samples. X lhsnorm (mu,sigma,n) returns an n -by- p matrix, X, containing a Latin hypercube sample of size n from a p -dimensional multivariate normal distribution with mean vector, mu, and covariance matrix, sigma. LHS is built as follows: we cut each dimension space, which. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. It is among the most popular sampling techniques in computer experiments thanks to its simplicity and projection properties with high-dimensional problems. In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. Time Series Analysis and Forecast (TSAF). The LHS design is a statistical method for generating a quasi-random sampling distribution. The LHS samples are continuous and uniformly distributed on each margin. MATLAB TOOLBOXES: TIME-SERIES ANALYSES, PORTFOLIO OPTIMIZATION AND LATIN HYPERCUBE SAMPLING. Let's say I want to take a LHS of 4 samples on 2 parameters. Perhaps to answer your question, it would help to create a small example.