Quality of Pseudo-Random Number Generators

Luke Ong just pointed out the following paper to me:

Click, Timothy H., Aibing Liu, and George A. Kaminski. "Quality of random number generators significantly affects results of Monte Carlo simulations for organic and biological systems." Journal of computational chemistry 32.3 (2011): 513-524.

I just wanted to check if this might be something that could affect us at all. (I assume this has been thought about and checked very carefully, but wanted to ask, just to be sure.)

I assume that the crucial random number generators used for inference of parameters are of high quality? The _rng’s used for generated quantities presumably aren’t quite as critical as they are only used for forward sampling. However, they might also be of more variable quality?

We’re using boost::ecuyer1988. We haven’t ever had any problems. Can you summarize how you think we should be testing?

@bgoodri at one point suggested an alternative: https://github.com/stan-dev/stan/issues/403

But I didn’t want to add more dependencies.