Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [latin-hypercube]

Latin hypercubes are stratified random samples of multi-dimensional space such that all strata of each marginal dimension are sampled exactly once.

References:

  • McKay, M.D.; Beckman, R.J.; Conover, W.J. (May 1979). "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code". Technometrics. 21 (2): 239–245.
  • Stein, M. (May 1987). "Large Sample Properties of Simulations Using Latin Hypercube Sampling" Technometrics. 29 (1): 143:151.
  • Tang, B. (Dec 1993). "Orthogonal Array-Based Latin Hypercubes". Journal of the American Statistical Association. 88 (424): 1392–1397.
  • Owen, A.B. (1992). "Orthogonal arrays for computer experiments, integration and visualization". Statistica Sinica. 2: 439–452.
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Are non-square latin hypercubes viable?

At https://github.com/OpenMDAO/OpenMDAO-Framework/issues/599 it is stated that non-square Latin Hypercube experimental design is not well defined (I assume that for higher dimensions that means hypercube must have the same length in every…
naught101
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Latin Hypercube Sampling Asymptotics

I am trying to construct a proof for a problem I am working on and one of the assumptions that I am making is that the set of points I am sampling from is dense over the entire space. Practically, I am using Latin hypercube sampling to obtain my…
user30490
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Is Latin hypercube sampling effective in multiple dimensions?

I am currently using a Latin Hypercube Sampling (LHS) to generate well-spaced uniform random numbers for Monte Carlo procedures. Although the variance reduction that I obtain from LHS is excellent for 1 dimension, it does not seem to be effective in…
Berk U.
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Increase the sample size of a Latin Hypercube study?

I want to create a climate model ensemble, testing 5 parameters (real, uniformly distributed between two values), using a latin hypercube approach. The problem is that I'm not sure how many replications I want to do. Is it viable to do one latin…
naught101
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Introductory Statistics and Basic Experimental Designs for Computer Scientists

I'm looking books on Introductory Statistics and Basic Experimental Statistics (Designs) for Computer Scientists. I'd highly appreciate if you point out few. Thanks Edited Actually I've been given the responsibility to teach: Stat-700 Elements of…
MYaseen208
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Choosing the number of latin hypercube samples

I'm using latin hypercube sampling to draw parameter values for an epidemiological simulation model (about 30 parameters, following various distributions), and so far I haven't been able to find any good rule of thumb/heuristics/theory for choosing…
cjauvin
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Effectiveness of Latin Hypercube Sampling

I have a question regarding the disccusion on the effectiveness of LHS in multiple dimensions, linked below. {Is Latin hypercube sampling effective in multiple dimensions?} According to the accepted answer, it appears that LHS starts to lose its…
ss_19
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Is there a way to check if sample obeys the Latin Hypercube Sampling rule?

I was wondering if there is a way to check if a certain sample of a large size obeys the Latin Hypercube Sampling rule. I know that for smaller samples, I can easily visualize the sample points to see if they are stratified according to the Latin…
ss_19
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How to generate a design for a response surface with a discrete input random variable?

I'm trying to generate a design of experiments for fitting a response surface for a quantity $Y$ such that, $Y = f(X_1, ..., X_6)$. I'm open to a factorial design as well as a random design. $X_1,..., X_5$ are continuous valued with specified upper…
Shihab Khan
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Latin hypercube sampling with categorical variables

I would like to run sensitivity analyses on my agent-based model. My model has 20 parameters that I need to vary. I generated 8 artificial landscapes that vary in resource aggregation (r) and my model runs on these landscapes. I used a Latin…
Nell
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Is it valid to use latin-hypercube sampling in parallel sampling?

I am sampling from a model 10 times in series, doing this in 50 parallel processes. I am using LHS to generate samples each set of ten samples, although each of the 50 parallel runs' samples are generated independently. Will using LHS sampling in…
kilojoules
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Why using MCMC, not LHS (Latin Hypercube Sampling)?

Let's say I have to find the posterior distribution of a Bayesian estimate. Why should I use an MCMC chain of length 10,000 but not do a Latin Hypercube Sampling of 10,000 samples and calculate* the corresponding posterior distribution values? What…
Safwan
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Is a group of random hypercube samples equivalent to a single latin hypercube with more samples?

Let's say, for the sake of argument, that you want a latin hypercube sample with 1,000 samples. For a later computational step, it would be more convenient to have a group of ten sets of 100 samples each, rather than a single massive set. Are those…
Fomite
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When is Latin Hypercube Sampling (LHS) a good idea?

In this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf [1] equation 6 shows that if $\operatorname{ cov} \left(f\left(x_1\right),f\left(x_2\right)\right)$ is positive LHS does not reduce random sampling…
kilojoules
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Using Latin Hypercube Sampling with a condition that the sum of two variables should be less than one

I am building an experimental design with 4 variables defined on (0,1). In notation, $x_i \in [0,1]$ with $ i=1,..., 4$). Two of these variables must satisfy the condition that $x_1 + x_2 \leq 1$. How can I perform Latin Hypercube Sampling with…
rms
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