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This question already has an answer here:

Can someone explain this to me: "the integral of [the Bayes estimator of] h(θ) does not have a closed form integral under the possibly closed form posterior distribution." It's from here: https://www2.isye.gatech.edu/~brani/isyebayes/bank/handout9.pdf.

More specifically:

  1. What is a closed-form integral?

  2. How do I know whether the integral of a function has a closed-form integral or not?

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marked as duplicate by Tim Jul 24 '18 at 5:59

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ You can determine if a particular function is closed form by doing the math. Sometimes you can just Google whether it's closed form. But for practical applications you usually do not care and simply use MCMC using your favorite software. $\endgroup$ – Tim Jul 24 '18 at 6:01
  • $\begingroup$ The discussion that you provided a link to does not discuss how you determine whether an integral is closed-form or not. Your comment itself does not offer much in the way of guidance. $\endgroup$ – Namenlos Jul 24 '18 at 6:33
  • $\begingroup$ Do you mean how to know for sure whether a closed form integral exists or not when you haven't been able to find one? That's an interesting question, but more for Maths SE than for CV. See How can you prove that a function has no closed form integral?. $\endgroup$ – Scortchi Jul 24 '18 at 8:50