# 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 hypercube of 20 samples, and then another of 10? How would I make sure the 30 samples are relatively evenly distributed? Or would it be possible to do 10-sized LHCs, and do multiples? ie. do 3 or 4 LHC samples of size 10, making sure that each LHC was independent of the others?

• Thanks for fixing the tag. I wanted to add the tag "latin-hypercube" instead of latin-square, but I don't have enough rep. Mar 15 '12 at 3:41
• – Abe
Mar 21 '12 at 1:21
• @Abe: you might also be interested in stats.stackexchange.com/questions/24978/… Mar 21 '12 at 1:23

With Latin hypercube samples, you have to decide on the number of samples, so that you break your range into either 10 or 20 bins to begin with. Otherwise, you will likely miss some parts of your space. My understanding is that the only quasi-Monte Carlo method that allows to take the next sample (or next $N$ samples) easily without trying to figure out their dependence on the previously collected samples is Halton sequence. See the encompassing treatment in Niederreiter (1992).
In fact, as far as I recall from computational physics literature (most likely, it was in Morokoff and Caflisch (1995)), for the sequence of length up to about $6^d$ where $d$ is the dimension of your space, quasi Monte Carlo sequences do not show appreciable gains over the standard pseudo-random number generators. So you may not have to bother with LHC and agonize over the choice between 10 and 20 samples -- you can just start with any random number generator you have at hand, and keep adding new ones if you are not satisfied with the achieved precision.