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What are the advantages and disadvantages of Latin hypercube sampling over simple random sampling?

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If you use Monte Carlo simulation to estimate the uncertainty or variability of a complex system, you need to generate random samples of the input variables. But how do you choose the best sampling method for your problem? In this article, you will learn about the advantages and disadvantages of Latin hypercube sampling (LHS) over simple random sampling (SRS).

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Geoffrey Gelman

Chief Data Scientist at Model Meetings

1 What is LHS?

LHS is a sampling method that divides the range of each input variable into equal intervals and selects one value from each interval. The values are then paired randomly to form the sample points. This way, LHS ensures that each interval is represented in the sample and that the sample points are more evenly distributed than in SRS.

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2 What is SRS?

SRS is a sampling method that selects values for each input variable independently and uniformly from the entire range. SRS does not guarantee that each interval is represented in the sample or that the sample points are well-spaced. SRS can produce clusters or gaps in the sample space, which can affect the accuracy and efficiency of the simulation.

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3 What are the advantages of LHS over SRS?

LHS is advantageous compared to SRS, as it reduces the sampling error and variance of the simulation results, especially for small sample sizes, and captures extreme values and interactions of input variables better. Furthermore, LHS improves the design and robustness of the simulation experiments, allowing for more flexibility and control over the sampling scheme. It can also be combined with other techniques such as stratification, orthogonalization, or optimization to enhance the quality and diversity of sample points. Additionally, LHS simplifies the analysis and interpretation of simulation outputs by reducing correlation and dependence among sample points. It also facilitates the use of regression or metamodeling methods to approximate the simulation function.

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4 What are the disadvantages of LHS over SRS?

Latent Hypercube Sampling (LHS) has some drawbacks compared to Simple Random Sampling (SRS). For instance, LHS requires more computational effort and memory than SRS, as it involves sorting, pairing, and randomizing the values for each input variable. Furthermore, LHS may be difficult to implement for high-dimensional or continuous problems. Additionally, LHS can introduce some bias or distortion in the simulation results, especially for non-linear or non-monotonic systems. It can also overestimate or underestimate the importance or sensitivity of some input variables, depending on how they are paired or ordered. Finally, LHS may not be compatible or efficient with some simulation models or methods, such as dynamic or stochastic systems, variance reduction techniques, or adaptive sampling strategies. As a result, it may not capture the temporal or spatial variability or the feedback effects of the system.

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Geoffrey Gelman

Chief Data Scientist at Model Meetings
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The coincidence of two rare events can have an outsized or catastrophic effect. For example, a hurricane makes landfall during spring tide, a snow storm disrupts air travel during a pilot strike, or a smoke detector short-circuits right before a fire outbreak. On the positive side, an unexpected celebrity endorsement coupled with a lull in blockbuster movie releases may lead to overwhelming demand for a video game with consequent stress on game servers. Since LHS randomly pairs values of input variables, it may miss a particular pairing that generates the outsized impact. SRS may miss the pairing as well, but at least a sample that contains a single rare event will not preclude the selection of another sample with both rare events together.

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5 How to choose between LHS and SRS?

When determining which sampling method (LHS or SRS) is best for your simulation problem, there is no one-size-fits-all answer. Factors such as the nature and complexity of the system, the objective and scope of the simulation, and the resources and constraints available, should all be taken into account. To ensure you are using the best fit for your problem, it is important to compare and test different sampling methods and criteria. Additionally, other tools and techniques such as sensitivity analysis, validation, verification, or calibration can help to improve the quality and efficiency of your simulation.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What are the advantages and disadvantages of Latin hypercube sampling over simple random sampling?

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1 What is LHS?

2 What is SRS?

3 What are the advantages of LHS over SRS?

4 What are the disadvantages of LHS over SRS?

5 How to choose between LHS and SRS?

6 Here’s what else to consider

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