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In summary, LHS can be effective in low to moderate dimensions and especially for functions well approximated by additive functions. While serving as a consultant to Los Alamos National Laboratory during the summer of 1975, W. The actual variance reduction achieved (in comparison to IID sampling) will depend on how close your chosen function is to being additive. The randomized point set has the property that for each coordinate j, there is exactly one point with coordinate j in each interval on length 1/n. Each axis of the hypercube is divided into n intervals of length 1/n. The above discussion shows that the LHS method has been well studied and. Implements Latin Hypercube Sampling (LHS) with n points in the s-dimensional unit hypercube. Again, this is not inconsistent with your second graph. One alternative approach for sampling the Xi is called Latin Hypercube sampling. In particular, the LHS algorithm that I use to generate $N$ spaced out uniform random variables in $D$ dimensions is:įor each dimension $D$, generate a set of $N$ uniformly distributed random numbers $\)$. Seeing how LHS is a well-known variance reduction technique, I am wondering whether I may be misinterpreting the algorithm or misusing it in some way. Although the variance reduction that I obtain from LHS is excellent for 1 dimension, it does not seem to be effective in 2 or more dimensions. One well known space filling design is the Latin Hypercube sampling method, proposed by McKay et al. I am currently using a Latin Hypercube Sampling (LHS) to generate well-spaced uniform random numbers for Monte Carlo procedures. This is a repository copy of On the use of a Modified Latin Hypercube Sampling (MLHS) approach in the estimation of a Mixed Logit model for vehicle choice.