- #Latin hypercube sampling uncertainty analysis manuals
- #Latin hypercube sampling uncertainty analysis free
It selects each point independently from the probability distribution for that input variable.
#Latin hypercube sampling uncertainty analysis free
(Feel free to skip this if you already understand Monte Carlo and LHS.) Monte Carlo (MC) simulation generates a random sample of N points for each uncertain input variable of a model. What is Latin Hypercube Sampling?įirst some background. Then I’ll add some key insights garnered from my own experience. Several of his complaints are specific to Crystal Ball or and don’t apply to Analytica. Let me explain why I disagree with David Vose on some issues and agree with him on others. And I’ve concluded that yes -it does make sense to keep Latin Hypercube as the default method. Monte Carlo on hundreds of real-world models. Why? Are we, the makers of these simulation products naïve? As the lead architect of Analytica for two decades, I’ve explored this question in detail. Interesting points, yet products like Analytica and Crystal Ball still provide LHS and even offer it as their default method. Marketing Evolution Leverages Analytica for Decision Analytics.Integrated assessment of climate change.From Controversy to Consensus: California’s Offshore Oil Platforms.Flood Risk Management in Ho Chi Minh City.Earthquake insurance – Cost-effective modeling.Bechtel SAIC and the Yucca Mountain Project.Are cows worse than cars for greenhouse gas?.Journal of the American Statistical Association. "Orthogonal column Latin hypercubes and their application in computer experiments". "Orthogonal arrays for computer experiments, integration and visualization". "Orthogonal Array-Based Latin Hypercubes". Latin hypercube sampling (program user's guide). Introduction, input variable selection and preliminary variable assessment". "An approach to sensitivity analysis of computer models, Part 1. "New approach to the design of multifactor experiments". "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code". Thus, orthogonal sampling ensures that the set of random numbers is a very good representative of the real variability, LHS ensures that the set of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just a set of random numbers without any guarantees. All sample points are then chosen simultaneously making sure that the total set of sample points is a Latin hypercube sample and that each subspace is sampled with the same density. In orthogonal sampling, the sample space is divided into equally probable subspaces.Such configuration is similar to having N rooks on a chess board without threatening each other. In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.One does not necessarily need to know beforehand how many sample points are needed. In random sampling new sample points are generated without taking into account the previously generated sample points.In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. This sampling scheme does not require more samples for more dimensions (variables) this independence is one of the main advantages of this sampling scheme. When sampling a function of N, to be equal for each variable. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column.
#Latin hypercube sampling uncertainty analysis manuals
Detailed computer codes and manuals were later published. An independently equivalent technique was proposed by Eglājs in 1977. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. The sampling method is often used to construct computer experiments or for Monte Carlo integration. Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution.