Skip to main content

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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
33 views

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 ...
user avatar
2 votes
1 answer
63 views

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 ...
Olle's user avatar
  • 21
3 votes
1 answer
369 views

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 <...
iwishiwasaneagle's user avatar
1 vote
1 answer
172 views

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 ...
Nishikido_MH's user avatar
2 votes
1 answer
263 views

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 ...
Christopher Klapperich's user avatar
1 vote
1 answer
134 views

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 ...
fitzberg's user avatar
  • 111
2 votes
1 answer
749 views

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 ...
Kevin's user avatar
  • 23
3 votes
1 answer
905 views

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 ...
Ant_C's user avatar
  • 31
1 vote
1 answer
127 views

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 ...
boyaronur's user avatar
  • 143
1 vote
0 answers
57 views

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 ...
Sadikov's user avatar
  • 31
2 votes
1 answer
184 views

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 ...
Ezequiel Castaño's user avatar
2 votes
2 answers
758 views

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 $x_1 + x_2 \leq 1$. ...
RMS's user avatar
  • 133
1 vote
1 answer
183 views

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 ...
AndreA's user avatar
  • 237
2 votes
1 answer
201 views

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 ...
ss_19's user avatar
  • 309
5 votes
2 answers
1k views

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 ...
ss_19's user avatar
  • 309
2 votes
1 answer
761 views

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 ...
ss_19's user avatar
  • 309
5 votes
1 answer
317 views

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 ...
ss_19's user avatar
  • 309
3 votes
1 answer
382 views

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 ...
ss_19's user avatar
  • 309
5 votes
1 answer
281 views

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,..., ...
Shihab Khan's user avatar
2 votes
1 answer
1k views

Taking samples of data using Latin Hypercube Sampling

Info: Newbie in Latin Hypercube Sampling (LHS) I have a number of variables/parameters that have different number of elements: $A = [1,2,3],$ $B = [1,2],$ and $C = [1,2,3,4]$ From these arrays I ...
jAdex's user avatar
  • 123
5 votes
3 answers
339 views

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 ...
Fomite's user avatar
  • 23.3k
1 vote
1 answer
526 views

Stopping rule for Latin hypercube sampling (LHS)

I'm a rookie of the statistics environment. I am looking for a "stopping rule" (or number of simulations required to get convergence) for Latin Hypercube Sampling (LHS) simulations. Normally, for ...
gionalim's user avatar
5 votes
1 answer
1k views

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 ...
Nell's user avatar
  • 133
0 votes
1 answer
231 views

Algorithmic or structural limitations of space-filling Latin hypercube sampling

I'm new to Latin hypercube sampling, and am trying to understand if the somewhat odd sampling that results from the Matlab function lhsdesign is a limitation of the ...
TTT's user avatar
  • 101
5 votes
1 answer
347 views

Latin Hypercube around set points

Is there a method for constructing a LHC around set points? For example, I want to test a component in a system and I have enough time to run 20 conditions. I expect that in the system, the component ...
Scott's user avatar
  • 51
4 votes
0 answers
1k views

Can a Latin Hypercube Sampling design include constraints relating the variables?

I am trying to generate an experimental design using a Latin hypercube on three dimensions. I'm using MATLAB's lhsdesign(), but my question is about lhs sampling in general. Two of my three variables,...
Ceph's user avatar
  • 318
0 votes
0 answers
151 views

Method for Sampling High Dimensionality Simulation (similar to Latin Hypercube Sampling)

I need to calculate the expected outputs (Yj) from a large non-linear simulation model (Mj) which takes 2^N possible input strings (Bi), each with known probability fi (simple binomial). N is ...
Simon Woodward's user avatar
5 votes
1 answer
1k views

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 ...
kilojoules's user avatar
4 votes
1 answer
2k views

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 ...
kilojoules's user avatar
4 votes
1 answer
993 views

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 ...
Safwan's user avatar
  • 255
1 vote
0 answers
64 views

Design on irregular domain

I am trying to get a design over some input parameters for a computer model, saying an input vector $X=(X_1,...,X_k)$. The domain of $X$ is irregular, not a hypercube (so I guess conventional Latin ...
Eridk Poliruyt's user avatar
6 votes
2 answers
214 views

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 ...
1 vote
0 answers
119 views

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? ...
Loukas Kt.'s user avatar
12 votes
2 answers
3k views

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 ...
user avatar
3 votes
1 answer
523 views

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 ...
wqp89324's user avatar
2 votes
2 answers
3k views

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 ...
Dan's user avatar
  • 1,150
8 votes
1 answer
6k views

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 ...
Asal's user avatar
  • 81
7 votes
1 answer
2k views

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 ...
naught101's user avatar
  • 5,461
15 votes
1 answer
785 views

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 ...
naught101's user avatar
  • 5,461
8 votes
3 answers
7k views

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 ...
Berk U.'s user avatar
  • 5,075
6 votes
0 answers
698 views

Choosing the number of latin hypercube samples [closed]

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 ...
cjauvin's user avatar
  • 613