by David Vose

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 (even though the @RISK manual describes LHS as “a new sampling technique”) 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.

However, desktop computers are now at least 1,000 times faster than the early 1980s, and the value of LHS has disappeared as a result. LHS does not deserve a place in modern simulation software. We are often asked why we don’t implement LHS in our ModelRisk software, since nearly all other Monte Carlo simulation applications do, so we thought it would be worthwhile to provide an explanation here.

What is 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…