1. Prabhas Chongstitvatana1 Monte Carlo integration It is a numerical probabilistic algorithm ab I/(b-a) f

2. Prabhas Chongstitvatana2 I/(b-a) b-a MCint(f,n,a,b) sum = 0 For i = 1 to n do x = uniform(a,b) sum = sum + f(x) Return ( b-a) * (sum/n)

3. Prabhas Chongstitvatana3 Variance of the estimate is inverse proportion to n The expected error is proportion to A deterministic algorithm for integration will sample at regular interval.

4. Prabhas Chongstitvatana4 DETint(f,n,a,b) sum = 0 delta = (b-a)/n x = a + delta/2 For I = 1 to n do sum = sum + f(x) x = x + delta Return sum * delta

5. Prabhas Chongstitvatana5 Advantage of MCint when doing multiple integral in high dimension. As the sample point increases exponentially with the dimension. Example 100, 100x100, 100x100x100. MCint is faster than a deterministic algorithm for dimension >= 4.