In a seminar, in a passing moment a presenter mentioned that multiple integrals over random variables is NP-Hard. This means there is no efficient algorithm to compute the integral.
So
Theorem: Integral of p(x1, x2, x3,...,xn) over x1, x2, ...., xn is np hard.
A preliminary search over the internet didn't give anything to see.
My question is:
Is it correct? It looks like correct because in many machine learning models they say that estimating max likelihood over latent variables is np-hard, so can't do it, but I don't really feel confident asserting this.
How to go about proving (showing the operation to be of exponential complexity) or disproving the result?
Are there tractable or intractable probability distributions too? What do they imply?