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Which Monte-Carlo methods are available for computing a multidimensional integral with Delta distributions (in case one cannot sample them explicitly)?

PS: I also asked a similar question at mathoverflow

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cannot sample what explicitly? The link in your linked MO question is much more detailed. Why not putting an excerp here? – draks ... Jul 24 '12 at 12:27
Typically, presence of the delta function indicates that you can carry out integration with respect to one variance explicitly. Do this and let numerical methods deal with the remaining integral. This may mean you would need to solve non-linear equations at each sampling point (depending on what is inside of the delta distribution). – Sasha Jul 24 '12 at 12:53
@Sasha thank you for the answer. That's what I tried to do. However the resulting equations are generally unsolvable (and there is a proof for that). Thus one cannot find the locations of such delta functions. I incline towards the mollification of the integrand, which would allow simultaneous (consistent) integration and the search for such "modes" with simmulated annealing embedded into this process. – Anton Aug 22 '12 at 7:24

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