Imagine you have a target probability distribution and you want to estimate the expectation . That’s lovely and everything, but if it was easy none of us would have jobs. High-dimensional quadrature is a pain in the arse. A very simple way to get an decent estimate of is to use importance sampling, that is taking draws , from some proposal distribution . Then, noting that we can use Monte Carlo to estimate the second integral. This leads to the importance sampling estimator This all seems m...
