I fear this question may be stupid, but yesterday I got an email from an engineer with these sentences in it:
Subset simulation is a sampling method for estimating failure probabilities. The task of estimating a failure probability is not an optimization problem; it is an estimation problem.
I as an old idiotic mathematician always thought that every statistical estimation problem (excluding pathological cases) can be formulated as an optimization problem.
Maybe I am wrong?
Can anybody of you enlighten me?