# Latin hypercube sampling with inequality constraints

@article{Petelet2009LatinHS, title={Latin hypercube sampling with inequality constraints}, author={Matthieu Petelet and Bertrand Iooss and Olivier Asserin and Alexandre Loredo}, journal={AStA Advances in Statistical Analysis}, year={2009}, volume={94}, pages={325-339} }

In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS… Expand

#### 61 Citations

Comparing and generating Latin Hypercube designs in Kriging models

- Mathematics
- 2010

In Computer Experiments (CE), a careful selection of the design points is essential for predicting the system response at untried points, based on the values observed at tried points. In physical… Expand

A Tutorial on Latin Hypercube Design of Experiments

- Computer Science
- Qual. Reliab. Eng. Int.
- 2016

This paper provides a tutorial on Latin hypercube design of experiments, highlighting potential reasons of its widespread use and going all the way to the pitfalls of the indiscriminate use of Latin hyper cube designs. Expand

An improved LHS approach for constrained design space based on successive local enumeration algorithm

- Computer Science
- 2019 IEEE 9th Annual International Conference on CYBER Technology in Automation, Control, and Intelligent Systems (CYBER)
- 2019

This paper proposes an improved algorithm of SLE-LHS, which taking into account constraints between the sample variables and can be used in the constrained space, and results of 2-D and 3-D sampling in constrained design space indicate that the S LE-CLHS approach performs well both in space-filling and in projection. Expand

Weighted space-filling designs

- Computer Science
- J. Simulation
- 2013

A method is proposed that incorporates known dependencies between input variables into design selection for simulators and the benefits of this approach via a simulator for atmospheric dispersion are demonstrated. Expand

Computer experiments: a review

- Mathematics
- 2010

In this paper we provide a broad introduction to the topic of computer experiments. We begin by briefly presenting a number of applications with different types of output or different goals. We then… Expand

Simulation of Constrained Variables in Engineering Risk Analyses

- Mathematics
- 2018

ABSTRACT The problem of sampling random variables with overlapping pdfs subject to inequality constraints is addressed. Often, the values of physical variables in an engineering model are… Expand

Representative Variable Annuity Policy Selection using Latin Hypercube Sampling

- 2013

Valuation and risk management of large portfolios of variable annuity policies are a big challenge to insurance companies because pricing a large portfolio of variable annuity policies is a time… Expand

Optimal design of computer experiments for surrogate models with dimensionless variables

- Mathematics
- 2017

This paper presents a method for constructing optimal design of experiments (DoE) intended for building surrogate models using dimensionless (or non-dimensional) variables. In order to increase the… Expand

Inverse problems occurring in uncertainty analysis

- Mathematics
- 2012

This thesis provides a probabilistic solution to inverse problems through Bayesian techniques.The inverse problem considered here is to estimate the distribution of a non-observed random variable X… Expand

Global sensitivity analysis in welding simulations-What are the material data you really need?

- Mathematics
- 2011

In this paper, the sensitivity analysis methodology is applied to numerical welding simulation in order to rank the importance of input variables on the outputs of the code like distorsions or… Expand

#### References

SHOWING 1-10 OF 54 REFERENCES

Large sample properties of simulations using latin hypercube sampling

- Mathematics
- 1987

Latin hypercube sampling (McKay, Conover, and Beckman 1979) is a method of sampling that can be used to produce input values for estimation of expectations of functions of output variables. The… Expand

Comparing and generating Latin Hypercube designs in Kriging models

- Mathematics
- 2010

In Computer Experiments (CE), a careful selection of the design points is essential for predicting the system response at untried points, based on the values observed at tried points. In physical… Expand

A Central Limit Theorem for Latin Hypercube Sampling

- Mathematics
- 1992

SUMMARY Latin hypercube sampling (LHS) is a technique for Monte Carlo integration, due to McKay, Conover and Beckman. M. Stein proved that LHS integrals have smaller variance than independent and… Expand

Latin Hypercube Sampling

- Computer Science
- 2008

This chapter discusses the use of computer models for such diverse applications as safety assessments for geologic isolation of radioactive waste and for nuclear power plants; loss cost projections… Expand

Optimal Latin-hypercube designs for computer experiments

- Mathematics
- 1994

Abstract Latin-hypercube designs (Lhd) were considered by Mckay et al. (1979) as designs for computer experiments. Sacks et al. (1989a) and Shewry and Wynn (1987) proposed optimal designs for… Expand

Optimal Latin hypercube designs for the Kullback–Leibler criterion

- Mathematics
- 2010

Space-filling designs are commonly used for selecting the input values of time-consuming computer codes. Computer experiment context implies two constraints on the design. First, the design points… Expand

Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems

- Computer Science
- 2002

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity… Expand

Computer experiments: a review

- Mathematics
- 2010

In this paper we provide a broad introduction to the topic of computer experiments. We begin by briefly presenting a number of applications with different types of output or different goals. We then… Expand

Numerical studies of the metamodel fitting and validation processes

- Computer Science, Mathematics
- 2010

A numerical approach is adopted to compare the performance of different types of space filling designs, in the class of the optimal Latin hypercube samples, in terms of the predictivity of the subsequent fitted metamodel, and concludes that such samples with minimal wrap-around discrepancy are particularly well-suited for the Gaussian process metAModel fitting. Expand

Comparison of designs for computer experiments

- Mathematics
- 2006

Abstract For many complex processes laboratory experimentation is too expensive or too time-consuming to be carried out. A practical alternative is to simulate these phenomena by a computer code.… Expand