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Jun 22, 2022 at 9:20 comment added Xi'an "Probability function" has no particular meaning in this setting. For rare events, cross-entropy is a way to build a better proposal than $p(\cdot)$
Jun 22, 2022 at 0:48 comment added Glen_b There are many potential algorithms that might be used. If you can find a suitable envelope for $q$ there's accept-reject (and a variety of potential ways to obtain some). If you have a suitable approximation to use in a proposal distribution and don't mind dependence in your generated values you may be able to use Metropolis-Hastings. etc etc
Jun 21, 2022 at 5:28 comment added kykim @jbowman For the specific problem I'm looking at, it's more a scoring function whose output is in [0, 1] e.g., $f(x)$ being how likely $x$ to meet some criteria. Perhaps I shouldn't have called $f$ a probability function.
Jun 21, 2022 at 1:27 comment added jbowman Is $f$ a probability density or a cumulative density?
S Jun 21, 2022 at 0:20 review First questions
Jun 21, 2022 at 1:19
S Jun 21, 2022 at 0:20 history asked kykim CC BY-SA 4.0