Using low-discrepancy sequence for bernoulli trials in MC sim

Question

I need to generate binomial distribution random numbers for my Carlo simulation (I need Bernoulli trials for a parameter). Thus far, I've used "rbinom" function for that. However, as I understand, I can more effectively use the parameter space by utilizing a low-discrepancy sequence for generating random numbers.

Is it possible to use Sobol sequence to generate Binomial random numbers? Or does it even make sense? If yes, then how to convert the sobol sequence to bernoulli or binomial distribution?

Thanks!

Answer 1

Monte Carlo methods are essentially a numerical integration method. Any numerical integration method can be substituted, for example, rectangle rule, Newton-Cotes, or integration via low-discrepancy sequences. When you use a low-discrepancy sequence, there isn't any sense in which you are simulating a random variable, but that is unimportant; what is important is that you are estimating an integral.

I assume that you have to make a lot of samples of a binary variable. You can treat that as a vector of values, e.g. (0, 1, 0, 1, 1, 0, ...). You could interpret that as a number between 0 and 1 and therefore map numbers in a low-discrepancy sequence into that. So to answer your specific question, yes, I think you can do that. However, it's not clear to me that there will be any benefit from it. It won't hurt to try if you have time, but on the other hand, I don't expect it to help much, if any.