Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I currently use a Halton sequence to choose parameter sets for a prognostic model (e.g. using metabolic rate and protein content parameters to predict growth rate).

From my understanding, both a Halton sequence and a Latin Hypercube can be used to evenly sample parameter space.

I am reviewing a paper where the author uses a Latin hypercube in the same context that I am using a Halton sequence.

How are these approaches related? Are there conditions under which one would be more appropriate?

share|improve this question
    
They're both "low discrepancy sampling methods", but the two algorithms look different to me... experimentation would probably be needed to see which of LH and Halton (and other sequences like Sobol and Niederreiter) would be best for your application. –  J. M. Apr 25 '11 at 16:16
    
Like J.M. says, it depends. What type of problem are you using them to solve? Numerical integration? Optimization/search? One drawback of Latin Hypercube is the inability to perform incremental sampling. If you're analyzing error in terms of the discrepancy of the samples, it makes sense to choose the method with lowest discrepancy measure (not sure what discrepancy of Latin hypercube is, but I have a feeling Halton beats it). –  dls Nov 29 '11 at 2:29
    
Another drawback of both techniques is whenever you want to look at multi-point correlations -- both techniques don't let the points cluster as much as a truly random selection would. I believe the Halton sequence does better. –  Craig Nov 29 '11 at 13:12
    
@dls my problem is that I want to minimize the number of samples required to estimate a multivariate likelihood surface. –  Abe Nov 29 '11 at 14:54

1 Answer 1

I am not aware of any theoretical results which allow a comparison to be made (unless you can compare discrepancy measures). I spent a good amount of time digging through the literature in the context of numerical integration, though I'm not an expert. I wasn't looking specifically for an answer to your question, but it was always in the back of my mind. Here are two papers which make experimental comparisons between sampling methods. The first would probably be of most interest to you.

L. P. Swiler, R. Slepoy, A. A. Giunta, Evaluation of sampling methods in constructing response surface approximations, Sandia National Laboratories.

Saliby, E., Pacheco, F., An empirical evaluation of sampling methods in risk analysis simulation: quasi-Monte Carlo, descriptive sampling, and latin hypercube sampling, Simulation Conference, 2002. Proceedings of the Winter.

share|improve this answer
    
thank you for helping me find the relevant literature –  Abe Dec 5 '11 at 20:06

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.