Latin hypercube sampling explained software#
Latin hypercube sampling explained free#

random () * segmentSize ) pointValue = ( point * ( variableMax - variableMin )) + variableMinДЇor our 2-by-4s, this might provide values like this: Sample Sampling: from _future_ import division import random iterations = 10 segmentSize = 1 / iterations for i in range ( iterations ): segmentMin = i * segmentSize #segmentMax = (i+1) * segmentSize point = segmentMin + ( random. (A common practice for Monte Carlo simulations is to start with about a thousand iterations, and work upwards depending upon the complexity of the problem.) WeвЂ™re also going to use Python to do our simulation. WeвЂ™re going to run this simulation with 10 iterations. All possibilities are equally likely (uniform distribution). The 2-by-4 (our first variable) comes in pieces 4cm to 40cm long, and the baseboards come in pieces 2cm to 60cm long. HeвЂ™s going to make the base out of a chunk of 2-by-4, and the sides out of baseboards. JoeвЂ™s odd U shaped picture frames require three pieces of wood. Joe wants to build U shaped picture frames out of these pieces, and heвЂ™s interested in knowing how probable it is that he can build a picture frame big enough for some strange purpose. They tend to cut pieces up for customers and always have leftovers that nobody is interested in because the ends are damaged, or other contrived reasons.

Latin hypercube sampling explained free#

ExampleДЄverage Joe has been offered free wood scraps from the local lumber yard. Independant uniform selection is done on each of the variableвЂ™s generated values. Once each variable has been sampled using this method, a random grouping of variables is selected for each Monte Carlo calculation. How this is done is different for every distribution, but itвЂ™s generally just a matter of reversing the process of the probability function. P(X <= x) = n is solved for x, where n is the random point in the segment. This number would be used to calculate the actual variable value based upon its distribution.

For the second segment, a number would be chosen between 0.2% and 0.4%.

For the first segment, a number would be chosen between 0.0% and 0.2%. A probability is randomly picked within each segment using a uniform distribution, and then mapped to the correct representative value in of the variableвЂ™s actual distribution.ДЄ simulation with 500 iterations would split the probability into 500 segments, each representing 0.2% of the total distribution. To perform the stratified sampling, the cumulative probability (100%) is divided into segments, one for each iteration of the Monte Carlo simulation. A cumulative frequency plot of вЂњrecovery factorвЂќ, which was log-normally distributed with a mean of 60% and a standard deviation of 5%. 500 samples were taken using the stratified sampling method described here, which generated a very smooth curve.ДЇigure 2.

Latin hypercube sampling explained software#

Differences within the plot, such as the left axis label and the black lines, are due to ongoing development of the software application and are not related to the issue being demonstrated.)ДЇigure 1. (These figures were generated using different versions of the same software.

Figure 1 and figure 2 demonstrate the difference between a pure random sampling and a stratified sampling of a log-normal distribution. The sampling algorithm ensures that the distribution function is sampled evenly, but still with the same probability trend.

Variables are sampled using a even sampling method, and then randomly combined sets of those variables are used for one calculation of the target function. The concept behind LHS is not overly complex. There are many resources available describing Monte-Carlo ( history, examples, software). Monte-Carlo simulations provide statistical answers to problems by performing many calculations with randomized variables, and analyzing the trends in the output data. LHS can be incorporated into an existing Monte Carlo model fairly easily, and work with variables following any analytical probability distribution. The method commonly used to reduce the number or runs necessary for a Monte Carlo simulation to achieve a reasonably accurate random distribution. Latin hypercube sampling (LHS) is a form of stratified sampling that can be applied to multiple variables.