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)
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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)
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3
Q

Properties of a Control Variable

A
  • known mean

- correlated with X

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