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I've read several sources of information that describe the process of Bayesian Monte Carlo Quadrature but am just not understanding the details enough to be able to implement it.

For instance two sources:

I get some high level ideas like:

  • It uses prior information better than other monte carlo algorithms such as Quasi Monte Carlo.
  • It can converge faster as a result, for integrands that are smooth.
  • It gives you a "confidence interval" so you can get an idea of how much variance / noise there is.
  • It seems to somehow use gaussian functions as basis functions.
  • every data point somehow fits the sum of gaussian basis functions to the actual function better?

Honestly, other than that it is pretty hazy.

Can anyone explain in a simple way how you could integrate a function over a specific domain, using Bayesian Monte Carlo Quadrature? Or any links to drop dead simple explanations, or implementations would be helpful too.

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  • $\begingroup$ Are you asking for a textbook chapter here? It would be better if you formulated a specific, focused question about a single issues you're having. $\endgroup$ – Raphael Aug 16 '17 at 19:54
  • $\begingroup$ I'm hoping for an explanation that isn't a textbook chapter - those haven't helped thus far. Hoping for a simpler, more straight forward explanation than I've seen. I'll try to think of a more specific question though. $\endgroup$ – Alan Wolfe Aug 16 '17 at 21:27

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