But given a situation where exact integration is intractable (like chess or Go), I'm not too sure what the difference really is, because it is those cases (on first thought) where the uniform distribution is useful--if you can see to the end, you don't need to care about bias, right?
Put it this way - suppose I can cook up a deterministic quadrature rule, e.g. quasi monte carlo or an asymptotic expansion. I assert that the quasi monte carlo will work just as well as monte carlo, probably better if convergence is faster.
If I'm right, this is a situation of "yay for uniform distributions". If I'm wrong, it's a "yay randomness" situation. It's nice to know which situation you are in - if I'm wrong, there is no point cooking up better deterministic quadrature rules.
Incidentally, LCG is known to be useless for monte carlo due to significant autocorrelation. So it's quite possible that people using LCG are incorrectly estimating their evaluation term.
Also for me, it's nice to know these things just for theoretical purposes and to enhance my understanding.
Put it this way - suppose I can cook up a deterministic quadrature rule, e.g. quasi monte carlo or an asymptotic expansion. I assert that the quasi monte carlo will work just as well as monte carlo, probably better if convergence is faster.
If I'm right, this is a situation of "yay for uniform distributions". If I'm wrong, it's a "yay randomness" situation. It's nice to know which situation you are in - if I'm wrong, there is no point cooking up better deterministic quadrature rules.
Incidentally, LCG is known to be useless for monte carlo due to significant autocorrelation. So it's quite possible that people using LCG are incorrectly estimating their evaluation term.
Also for me, it's nice to know these things just for theoretical purposes and to enhance my understanding.