For no practical reason whatsoever, simply curious: Say you need to use Gaussian Process Regression to model some $x,y$ relationship. Now, suppose that you're interested in integrating over some interval $[a,b]$. My questions are:

  1. Does this computed area have any practical application (finance, logistics, etc.)?
  2. Should stochastic calculus be used or is it much simpler to simply use Monte Carlo Integration?

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