Latin hypercube sampling uncertainty analysis

#Latin hypercube sampling uncertainty analysis manuals

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.

#Latin hypercube sampling uncertainty analysis 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. This is clearly seen by comparing the two tabular data files.Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. The new samples will be combined with the original samples to generate a combined sample of size 20. The user will get 10 new LHS samples which maintain both the correlation and stratification of the original LHS sample. Tabular_data_file = 'lhs_incremental_20.dat' Where LHS_20.in is shown below, and LHS_10.rst is the restart file containing the results of the previous LHS study. Then an incremental LHS study can be run with: dakota -i LHS_20.in -r LHS_10.rst -w LHS_20.rst One way to ensure the restart file is saved is to specify a non-default name, via a command line option: dakota -i LHS_10.in -w LHS_10.rstДЄnd the restart file is written to LHS_10.rst. ExamplesДЇor example, say a user performs an initial study using lhs as the sample_type, and generates 10 samples. See the examples below and the Usage and Restarting Dakota Studies pages. The incremental approach is useful if it is uncertain how many simulations can be completed within available time.

binomial, Poisson, etc.) as well as histogram variables and uncertain set types. Incremental LHS sampling support both continuous uncertain variables and discrete uncertain variables such as discrete distributions (e.g. The variables and responses specifications must be the same in both studies. Additionally, a previous LHS (or incremental LHS) sampling study with sample size must have already been performed, and the dakota restart file must be available from this previous study. To change this behavior, the incremental_lhs keyword must be specified in conjuction with the sample_type keyword. Incremental Latin Hypercube Sampling is not used by default. The number of samples in the second set MUST currently be 2 times the number of previous samples, although incremental sampling based on any power of two may be supported in future releases. Incremental_lhs will augment an existing LHS sampling study with more samples to get better estimates of mean, variance, and percentiles. Number of samples from an already-completed sampling study Augments an existing Latin Hypercube Sampling (LHS) study SpecificationДefault: no sample reuse in coefficient estimation