stratified sampling latin hypercube sampling

#Stratified sampling latin hypercube sampling manuals#
#Stratified sampling latin hypercube sampling software#

Discrete version of LHS is also presented for reliability evaluation. Latin Hypercube sampling (LHS), which has many desirable features of stratified sampling and random sampling has been successfully applied to generation system reliability evaluation. Journal of the American Statistical Association. network and has no effect on the other system. 'Orthogonal column Latin hypercubes and their application in computer experiments'. 'Orthogonal arrays for computer experiments, integration and visualization'. Journal of the American Statistical Association. '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: Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. 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.

#Stratified sampling latin hypercube sampling manuals#

Detailed computer codes and manuals were later published. An independently equivalent technique was proposed by Eglājs 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. It can also be used to force the sampling of tails of distributions, although it should be remembered that LH stratification applies to each individual input variable, and it would not force the simultaneous sampling of tail values for more than one input.Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution.

In general, LH sampling would be favourable when testing and developing a model (running only a small number of iterations), or when running a model that is so large that only a small number of iterations can be conducted. for 1000 iterations, exactly one value above the P99.9 would be drawn, whereas for MC sampling either none, one or several samples may be drawn). a small number of iterations is used), and would also ensure that tail samples of the input distributions are drawn (e.g. It would avoid potential non-representative clustering of sampled values (particularly when small sample sizes are drawn i.e. In theory, LH sampling would create a more representative sampling of the distribution. the cumulative curve is divided into equal intervals on the cumulative probability scale (0 to 1.0). LH sampling involves a stratification of the input distribution i.e.

#Stratified sampling latin hypercube sampling software#

When using ( Monte Carlo software for risk analysis and risk assessment), a user may choose between the Monte Carlo (MC) and Latin Hypercube (LH) sampling types.