sampling techniques · winter 2011/2012 ms&e348/infanger 9 . variance reduction techniques •...

Sampling Techniques

MS&E348 Winter 2011/2012

Professor Gerd Infanger

Multidimensional integration

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Monte Carlo methods

• Monte Carlo Methods are promising for multidimensional integration • For example, determine the average height of a board:

v1

v2

Crude Monte-Carlo

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Motivational example: importance sampling

v1

v2

F1 F2

F = F1 + F2

z1, assume z2 = 0

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Variance reduction techniques

• Stratified sampling • Importance sampling • Control variates • Antithetic variates

Importance sampling

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The best importance distribution

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Additive and multiplicative approximation functions

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Multiplicative marginal cost model

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Variance Estimation

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Additive marginal cost model

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Sample size and variance

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Control variates

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Variance estimation

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Approximation functions

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