Latin Hypercube Sampling

Most risk analysis simulation software products offer Latin Hypercube Sampling (LHS). It is a method for ensuring that each probability distribution in your model is evenly sampled which at first glance seems very appealing.

The technique dates back to 1980 when computers were very slow, the number of distributions in a model was extremely modest and simulations took hours or days to complete. It was, at the time, an appealing technique because it allowed one to obtain a stable output with a much smaller number of samples than simple Monte Carlo simulation, making simulation more practical with the .

Computing tools available at the time.

What is Latin Hypercube sampling

** The Main Principle is to divide the Area Into Strata 

Latin Hypercube Sampling (LHS) is a type of stratified sampling. It works by controlling the way that random samples are generated for a probability distribution. Probability distributions can be described by a cumulative curve, like the one below. The vertical axis represents the probability that the variable will fall at or below the horizontal axis value. Imagine we want to take 5 samples from this distribution. We can split the vertical scale into 5 equal probability ranges: 0-20%, 20-40%, …, 80-100%. If we take one random sample within each range and calculate the variable value that has this cumulative probability, we have created 5 Latin Hypercube samples for this variable:

This methodology is used to generate more more accurate simulation results in general when comparing it with other simulation sampling methods, with lower standard errors level, with lower or fewer sampling trials.

this method was established in 1979 by the governmental research of statistical mathematics in united kingdom and set the reference to many developed methodologies in this field around the world, the idea was derived from developing the normal distribution changing under certain conditions by setting a limit of fixed data and facultative results.

The optimal Latin hypercube option generates a large number of random Latin hypercube designs, then iteratively improves each of them and uses the best of the improved designs. This is very effective at finding a good design, but requires additional processing time. For example, a 20-variable 300-evaluation design takes about five minutes of CPU time. Optimal Latin hypercube uses centered L2 discrepancy (a measure of uniformity) as the optimality criteria. If a time limit is specified in the study definition, HEEDS will stop improving the sampling design when the specified wall-clock-time limit is reached. HEEDS will use the best design found to that point.