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Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective

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arxiv 1506.00021 v1 pith:WLUMYYTA submitted 2015-05-29 cs.GR

Michael Kazhdan , Gurprit Singh , Adrien Pilleboue , David Coeurjolly , Victor Ostromoukhov This is my paper
classification cs.GR
keywords carlointegrationmontevarianceclosed-formrepresentation-theoretictheoryanalysis
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In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a more general theory. We review the related representation theory and show how it can be used to derive a closed-form solution.

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