# 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.

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### Optimizing Sampling Strategy to Enhance Uniformity Under Conditional Constraints

I am facing a challenge in a project that involves sampling from a design space defined by 10 variables. I use Latin Hypercube Sampling (LHS) and/or Sobol sequences, and initially, the samples are ...
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### Finding significant factors in a Latin Hypercube Design

I'm simulating data where I have four factors and one response that I want to examine. I have two different DoE designs, one 2⁴ factorial design and one Latin Hypercube Design. The ultimate goal with ...
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### Latin Hypercube Sampling of a Gaussian Process [closed]

I have a small set ( $n \approx 200$ ) $(x,y)$ data points representing the find location of a person on a landscape. From this, I generate a $20\times 20$ histogram and fit the fairly basic model <...
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### How could proving the result of variance of estimator in Latin Hypercube Sampling

Ok i almost freak out of this!!!! i've to doing some presented about this paper (M.D.MCKAY,J.BECKMAN, W.J.CONOVER (1979). It's about comparing methods for selecting values (Random Sampling, Stratifed ...
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### How to Analyze Latin Hypercube Results

After running an experiment generated by a Latin Hypercube design, what next? Just pick the best point? I guess there’s no ‘modeling’ or ‘curve fitting’ going on right? So you basically just choose ...
1 vote
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### Sampling points on the edges and corners of a hybercube via LHS

I am looking for some source that supports my intuition, that the Latin Hypercube Design rarely (or never?) samples points from the surface. A point lies on the surface of a hypercube if at least one ...
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### Latin hypercube sampling for both float and integers

I am using Latin hypercube sampling to generate the combinations of 5 parameters. In these 5 parameters, the values of two parameters can be float numbers, while the values of three parameters must be ...
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### Latin Hypercube Sampling with input correlation matrix in Python

I am attempting to take into account the interaction among 5 different parameters in a Latin hypercube design in Python 3.8. However, I can't understand how, probably also because - not being my field ...
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1 vote
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### Stratification of Random Walk Jumps in Metropolis-Hastings

I aim to achieve variance reduction in Random Walk Metropolis Hastings algorithm by introducing stratification to the random walk jumps. What I have tried is to make use of Latin Hypercube Sampling in ...
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### How many points for statistical significance in design of experiments

I am running an experiment that includes 27 input data points. The function yields results if we input $2 \leq x \leq 27$ points. I divide my data points in 9 sets of 3 points each. Now, I want to ...
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### Is it necessary to shuffle x coordinates in Latin Hypercube Sampling (LHC)?

I am dealing with some implementations details about LHC sampling and I found that the common algorithm is as follows: Determine the limits for each cell (row/column) Sample a random number in each ...
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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 $x_1 + x_2 \leq 1$. ...
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### Stratified sampling / QMC simulation for compound Poisson rv

I have a rv $X$ of the form $$X=\sum_{i=1}^N Y_i,$$ where $N$ is a discrete rv (often, but not always, Poisson) and $Y_1,\ldots,Y_N$ are continuous random variables, iid and independent from $N$. I ...
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### Dividing CDF rather than PDF equally in Latin Hypercube Sampling

Returning back to the basics of Latin Hypercube Sampling, I wanted to ask why LHS is a division of CDF into N intervals rather than PDF. I'm having some trouble understanding what the difference is ...
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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 ...
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### Convergence of random sample vs. Latin Hypercube Sampling

Latin Hypercube Sampling, by concept, should be able to yield convergence of an estimate of output at a lower number of samples than random sampling. With the model I am working on, I'm continuously ...
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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 ...
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### Number of parameter sets generated by latin hyercube sampling

In MATLAB, X = lhsdesign(n,p) generates a latin hypercube sample of n number of random parameter sets (n values on each of p variables). By the definition of latin hypercube sampling, there is a much ...
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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 ...
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### Offshore Wind Assessment

Does anyone know if Latin Hypercube sampling can be effective in the statistical analysis of offshore wind time series in order to reproduce random wind fields with a small amount of observed data? ...
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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 ...
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### Are Latin hypercube samples uncorrelated

I understand the basics to Latin hypercube sampling, such as implemented by the algorithm LHSA mentioned in the book Design and Modeling for Computer Experiments. But I'd like to make sure: 1, n ...
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### Is there an equivalent to LHS for a discrete input space?

I was wondering if there is a method that is equivalent to Latin Hypercube Sampling when the input space you are trying to sample from are a finite discrete set of possible values. For example, if I ...
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### How to determine the sample size of a Latin Hypercube sampling?

I am designing an experiment with 5 variables. Some of the variables have 2 and others have 3 levels. The method that I am going to use is the Latin Hypercube, but I do not not what the sample size ...
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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 ...
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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 ...
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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 ...
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