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I need to evaluate (numerically) a multi-dimensional integral of the form

[itex]\int_A f(x) dx[/itex].

Now in my application, I already have points inside the domain A which are distributed like [itex]\frac{f(x)}{\int_A f(x) dx}[/itex]. So I hoped I could use these random points in some importance sampling monte carlo integration technique, since this would not result in any additional computational cost.

However, using these random points for monte carlo integration doesn't seem so easy, since all ideas that came to my mind need the value of the normalizing constant [itex]\int_A f(x) dx[/itex]. Obviously, I don't have this value, since this is exactly what I want to compute.

Does anybody have an idea?

Best,

derivator

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# Numerical integration, use given random distribution as integration points

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