There are two algorithms that are the basis of probability distributions and statistical analysis. One is the Monte Carlo, which is the older of the two. The other is the Latin Hypercube.
Back story of the Monte Carlo Method
There’s an interesting back story to the invention of the Monte Carlo method. It was Stanislaw Ulam who first started playing around with this a long time ago, pre-World War II. He broke his leg and was in rehab for a long time, convalescing.
He played solitaire to pass the time, and wanted some way of figuring out what the probability was that he would finish his solitaire game successfully. He tried many different math techniques, but he couldn’t do it. Then he came up with this idea of using probability distribution as a method of figuring out the answer.
Years later, scientists working on the Manhattan Project were trying to figure out what the likelihood was for the distribution of neutrons for nuclear reaction. They remembered this method and used it to calculate something that they couldn’t figure out any other way. They needed a name for it. One of the guys on the team had an uncle that used to gamble a lot in Monte Carlo, so they decided to call it the Monte Carlo method in honor of the odds and probabilities found in casinos.
Differences Between the Monte Carlo Algorithm and the Latin Hypercube
When you run a Monte Carlo simulation or a Latin Hypercube simulation, what you’re trying to achieve is convergence. This is when you reach the point where you could run another ten thousand, or another hundred thousand simulations, and your answer isn’t really going to change.
Because of the way the algorithms are implemented, Latin Hypercube reaches convergence more quickly than the Monte Carlo. It’s a more advanced, more efficient algorithm for distribution calculations.
Which One Should I Use?
They’re both going to come to the same answer, so the choice comes down to familiarity. Older school risk assessment people are going to have more experience with the Monte Carlo, so they might default to that, whereas newer folks would naturally tend toward a more efficient algorithm.
They’re very similar. One is newer and faster, but with computer software there’s no extra work on anyone’s part. It’s really just a question of which method you are more comfortable with. We practice both.