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Latin hypercube

In Monte Carlo sampling for simulation problems, random values are generated from a probability distribution deemed appropriate for a given scenario (uniform, poisson, exponential, etc.).  In simple random sampling, each potential random value within the probability distribution has an equal value of being selected. Just due to the vagaries of random chance, clusters of similar values will occur, as well as “holes” in the distribution.  These will be subsumed over time as many more values are generated so that, in the long run, the simulated values will come closer and closer to the reference distribution. With Latin Hypercube sampling, the process is constrained so that the random values being generated represent the entire distribution.  For example, a value quite close to another value would be rejected as long as there are “holes” or under-represented regions. This allows more efficient sampling – the “long run” in which the sample comes to adequately represent the reference distribution is shorter than in the case of simple random sampling.