![]() Increasing sample size, the sampling error of 0.005 at a sample size of N=10,000-a one-hundred-fold increase in the number of samples. Here, the sampling error for MC is 20 times larger than for RLHS. I ran this sample of 100 points 10,000 times for each method and computed the standard deviation of the computed sample mean, as a measure of sampling error: RLHS and MC each end up with a non-zero value as a result of randomness in sampling, where MLHS estimates the mean as exactly zero. Consider this example: I generated a sample of N=100 points from a standard Normal(0,1) distribution using each method and computed the sample mean. People also use the term variance reduction. But the real question is how many samples do you need to get to a given level of precision? Or conversely, at a given sample size, how much sampling error is there in the computed results? The concept of convergence rate addresses these questions. You can make up for MC’s inefficiencies by increasing the sample size. MC and LHS are both unbiased estimation techniques: computed statistics approach their theoretical values as the sample size increases. PDF resulting from N=100 samples using each of the sampling methods. The impact of LHS is visually evident in the following Probability Density Graphs (PDFs) that are each created using Analytica’s built-in Kernel Density Smoothing method for graphing, using samples generated from MC, RLHS and MLHS. Random Latin Hypercube (RLHS) selects a random point within each interval. Analytica provides two variants: Median Latin Hypercube (MLHS) uses the median value of each equiprobable interval. It shuffles the sample for each input so that there is no correlation between the inputs (unless you want a correlation). It partitions each input distribution into N intervals of equal probability, and selects one sample from each interval. Latin Hypercube sampling (LHS) aims to spread the sample points more evenly across all possible values. You might end up with some points clustered closely, while other intervals within the space get no samples. Because it relies on pure randomness, it can be inefficient. From this random sample for each result, it estimates statistical measures such as mean, standard deviation, fractiles (quantiles) and probability density curves. It generates a sample of N values or scenarios for each result variable in the model using each of the of the corresponding N points for each uncertain input. ![]() ![]() It selects each point independently from the probability distribution for that input variable. (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. In a post on LinkedIn, David Vose argues that the advantages of Latin Hypercube sampling (LHS) over Monte Carlo are so minimal that “LHS does not deserve a place in modern simulation software.” He makes some 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?.
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