![]() ![]() However, the samples are not totally independent because they are constrained to have one sample from each of the n intervals. With random Latin hypercube sampling, each sample is a true random sample from the distribution, as in simple Monte Carlo. The random Latin hypercube method is similar to the median Latin hypercube method except that, instead of using the median of each of the m equiprobable intervals, it samples at random from each interval. These points are then randomly shuffled so that they are no longer in ascending order, to avoid nonrandom correlations among different quantities. The sample points are the medians of the m intervals, that is, the fractiles: Median Latin hypercube sampling is the default method: It divides each uncertain quantity X into m equiprobable intervals, where m is the sample size. You can therefore use standard statistical methods to estimate the accuracy of statistics, such as the estimated mean or fractile (percentile) of a distribution, as described in Selecting the Sample Size. With the simple Monte Carlo method, each value of every random variable X in the model, including those computed from other random quantities, is a sample of m independent random values from the true probability distribution for X. It then uses the inverse of the cumulative probability distribution to generate the corresponding values of X, ![]() Analytica generates m uniform random values, u i, for i = 1, 2.m, between 0 and 1, using the specified random number method (see below). In this method, each of the m sample points for each uncertainty quantity, X, is generated at random from X with probability proportional to the probability density (or probability mass for discrete quantities) for X. The most widely used sampling method is known as Monte Carlo, named after the randomness in games of chance, such as at the famous casino in Monte Carlo. 6 When not to use Latin hypercube sampling.
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