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(Importance sampling) Suppose we want to approximate the integral where we assume this integral…

(Importance sampling) Suppose we want to approximate the integral (Importance sampling) Suppose we want to approximate the integral where we assume this integral... where we assume this integral is finite. Let f be a density on the interval (a, b) such (Importance sampling) Suppose we want to approximate the integral where we assume this integral... and is such that we have a convenient algorithm for generating (Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

(a)    Prove that

(Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

We refer to f as an importance sampler and note this shows that every f satisfying the above conditions, provides a consistent estimator (Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

(Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

c) Suppose that g(x) = h(x) f (x), where f is as described above. Show that importance sampling with respect to f leads to the estimator

(Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

(d) Show that if there exist (Importance sampling) Suppose we want to approximate the integral where we assume this integral... 

(e) Determine the standard error of and indicate how you would use this to assess the error in the approximation M (Importance sampling) Suppose we want to approximate the integral where we assume this integral...