Slide 6
Slide 6 text
Intro IID Low Discrepancy Software Summary References
Computing the Mean, µ = E(Y)
Probability µ = y ϱ(y) dy, Y ∼ known ϱ
Computer Experiments Y = f(X), X ∼ U[0, 1]d
µ =
[0,1]d
f(x) dx ∈ [^
µ − ε, ^
µ + ε], ε specified, fixed width
^
µ =
1
n
n
i=1
f(Xi), X1, X2, mimic
∼ U[0, 1]d
Statistics µ ∈ ^
µ −
2.58^
σ
√
n
, ^
µ +
2.58^
σ
√
n
with high probability
^
µ =
1
n
n
i=1
Yi, ^
σ2 =
1
n − 1
n
i=1
(Yi − ^
µ)2,
Y1, Y2, . . . IID
∼ unknown ϱ
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