Week 6 Flashcards
1
Q
Idea of Variance Reduction Techniques
A
- Exploit controllability of random-number generator to recycle previously used random numbers and include some kind of correlation
- Basic relation used:
Var(aX + bY) = a^2Var(X) + b^2Var(Y) + 2abCov(X, Y) - If the last term is negative, then the variable could be reduced
- Cov(X,Y) = Σ(Xi - Xbar)(Yi - Ybar) / (n-1)
2
Q
Control Variates Method
A
- This method works by relating the r.v. of interest X to another r.v. with known mean Y
- E.g. in queueing simulation X could be delay time and Y service time
- Idea is to use knowledge of E(Y) to control X, when X and Y are correlated
- X(c) = X + c(Y-E(Y))
- By construction, E(X(c)) = E(X)
3
Q
Properties of a Control Variable
A
- known mean
- correlated with X