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Variance Analysis for Monte Carlo Integration

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Academic year: 2021

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Figure 1: Illustration of the random nature of the Fourier coefficients of a 1D white noise sampling pattern
Figure 2: Summary of theoretical power spectra and their convergence rate for the best case and worst cases of integration
Figure 3: Illustration of spherical sampling methods: Healpix underlying structure (a) used in regular sampling (b), stratified sampling (c) and our implementation of CCVT (d)
Figure 4: Bounds on the power spectra and on the variance convergence rate of our test integrands in the toroidal domain
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