![]() ![]() If this is done repeatedly, with many input samples drawn, one can build up a distribution of the output as well as examine correlations between input and output variables. Many simulation codes have input parameters that are uncertain and can be specified by a distribution, To perform uncertainty analysis and sensitivity analysis, random values are drawn from the input parameter distributions, and the simulation is run with these values to obtain output values. In some cases, the pairing is restricted to obtain specified correlations amongst the input variables. ![]() The high-dimensional LHD (HLHD) problem is one of the crucial issues and has been a large concern in the long run. A sample is selected at random with respect to the probability density in each interval, If multiple variables are sampled simultaneously, then values obtained for each are paired in a random manner with the n values of the other variables. Latin Hypercube Design (LHD) is widely used in computer simulation to solve large-scale, complex, nonlinear problems. In more » LHS, the range of each variable is divided into non-overlapping intervals on the basis of equal probability. Latin Hypercube A Latin square has the property that each of the three symbols A, B, and C, appear only once in each row and column of a two-dimensional. LHS is a constrained Monte Carlo sampling scheme. LHS UNIX Library/Standalone uses the Latin Hypercube Sampling method (LHS) to generate samples. I chose a LHS design rather a full factorial design in order to reduce the number of simulations. I used a Latin Hypercube Sampling design (LHS) to generate sets of parameters (N 100) used as inputs for the simulations. The LHS samples can be generated either as a callable library (e.g., from within the DAKOTA software framework) or as a standalone capability. In this exercise I have decided to use the so-called ‘latin hypercube’ sampling strategy. I generated 8 artificial landscapes that vary in resource aggregation (r) and my model runs on these landscapes. Its one disadvantage is that, sometimes, depending on the distribution, the inverse distribution function can be quite computationally expensive to calculate, with some requiring more effort than others. ![]() Multiple distributions can be sampled simultaneously, with user-specified correlations amongst the input distributions, LHS UNIX Library/ Standalone provides a way to generate multi-variate samples. It is the only method that will work with the so-called ‘latin hypercube’ sampling strategy. It performs the sampling by a stratified sampling method called Latin Hypercube Sampling (LHS). The LHS UNIX Library/Standalone software provides the capability to draw random samples from over 30 distribution types. ![]()
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