Monte Carlo Integration with R - UMD
Monte Carlo Integration with R
General idea:
We wish to integrate,
I(f)=Int_{a}^{b} f(x) dx
1. Choose a pdf g(x) on [a,b]. 2. Generate data X_1,X_2,...,X_n from g(x). 3. Estimate I(f) by:
1
f(X_i)
--- Sum_{i=1}^{n} --------
n
g(X_i)
1. I(f)=Int_{0}^{1}(phi(x)), phi(x) standard normal pdf. -------------------------------------------------------#Exact Answer: > pnorm(1)-pnorm(0) [1] 0.3413447
Monte Carlo: Since [a,b]=[0,1], we can use g(x) ~ Unif[0,1]
Integral ................
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