#Median latin hypercube sampling manuals#
#Median latin hypercube sampling windows#

Our example shows that 25 model runs based on selected retention curves could adequately approximate the results from our assumed truth (1000 LHS Monte Carlo simulations), while LHS alone required in excess of 50 realizations to achieve the same quality result. Convergence of the proposed sampling method was assessed by comparing statistics of breakthrough curves observed at a compliance boundary with those obtained using between Latin hypercube sampling (LHS) Monte Carlo simulations. The retention curve subsampling methodology was applied to three-dimensional simulations of conservative tracer transport beneath Material Disposal Area G at the Los Alamos National Laboratory. Instead of sampling each individual soil parameter from its probability space and then running Monte Carlo simulations using realizations of rock parameters directly, we calculate retention curves from realizations of rock parameters, take subsamples from these retention curves, and run simulations using parameter realizations corresponding to these selected retention curves. JSTOR 2670057.We have developed a new Monte Carlo sampling method for simulating flow and transport in unsaturated porous media, characterized by van GenuchtenвЂ“Mualem constitutive relations. Journal of the American Statistical Association. 'Orthogonal column Latin hypercubes and their application in computer experiments'. 'Orthogonal arrays for computer experiments, integration and visualization'. 'Orthogonal Array-Based Latin Hypercubes'. Latin hypercube sampling (program user's guide). Introduction, input variable selection and preliminary variable assessment'. 'An approach to sensitivity analysis of computer models, Part 1. 'New approach to the design of multifactor experiments'. 'A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code'. Thus, orthogonal sampling ensures that the set of random numbers is a very good representative of the real variability, LHS ensures that the set of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just a set of random numbers without any guarantees. All sample points are then chosen simultaneously making sure that the total set of sample points is a Latin hypercube sample and that each subspace is sampled with the same density.

In orthogonal sampling, the sample space is divided into equally probable subspaces.

Such configuration is similar to having N rooks on a chess board without threatening each other.

In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.

One does not necessarily need to know beforehand how many sample points are needed.

In random sampling new sample points are generated without taking into account the previously generated sample points.

In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows:

#Median latin hypercube sampling windows#

Both simulation options and the selection of model outputs are entered with Windows style menus, dialog boxes and use of the mouse. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. Both Monte Carlo and Latin Hypercube sampling techniques are supported, and distributions of possible results may be generated for any cell or range of cells in your spreadsheet model.

This sampling scheme does not require more samples for more dimensions (variables) this independence is one of the main advantages of this sampling scheme. When sampling a function of N, to be equal for each variable. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column.

#Median latin hypercube sampling manuals#

Detailed computer codes and manuals were later published. An independently equivalent technique was proposed by EglДЃjs in 1977. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. The sampling method is often used to construct computer experiments or for Monte Carlo integration. Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. WikiMili Latin hypercube sampling Last updated June 24, 2021