Simulation of super high-dimensional distribution

I am working on simulated method of moments which requires to draw random variables from a multivariate normal distribution for numerical integration. However, the dimension of this multivariate normal distribution is super high, something like 250000. I would like to use Halton sequence. Since the dimension is so high, I believe I need to use the so called scrambled Halton sequence to avoid highly correlated draws. I have three questions:

  1. Given the super high dimension, is there a better way of sampling?
  2. If I have to use scrambled Halton sequence, is there a Julia package for it?
  3. Given the super high dimension, is there a rule of thumb for the number of simulations for each observation?

I noticed the following post about Sobol sequences, but it seems that there is already some problem with a dimension of 100. So I am guessing it will be the same for Halton.

I noticed the following two Halton packages, but I don’t think they offer the option of scrambled Halton. Thank you.


Alternatively, you could just set a random seed and use plain old rand(). Either your problem is “nice” (insensitive to issues of non-uniform coverage), or both methods will be horrible anyway for 2.5e5 dimensions for a feasible number of draws.

I see. Thank you.

Regarding your second point, I don’t know what you’ve used before, but I use the randtoolbox R package to generate scrambled low discrepancy sequences, you can try to use it with RCall.