Variance analysis for Monte Carlo integration

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

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Variance Analysis for Monte Carlo Integration: Representation-Theoretic Perspective

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...

Monte Carlo Integration and Variance Reduction

Variance Analysis for Monte Carlo Integrationupplementary material

In this document, we provide supplementary details on various topics discussed from the main paper. In Sec. 2, we give a short background of the Representation theory framework that we used in our derivation for the spherical domain Monte Carlo (MC) variance formulation. In Sec. 3, we provide additional theoretical background of projective 2-space that allows spectral analysis of hemispherical ...

Sampling and Variance Analysis for Monte Carlo Integration in Spherical Domain. (Analyse de Variance et Échantillonnage pour l'intégration Monte Carlo sur la sphère)

This dissertation introduces a theoretical framework to study different sampling patterns in the spherical domain and their effects in the evaluation of global illumination integrals. Evaluating illumination (light transport) is one of the most essential aspect in image synthesis to achieve realism which involves solving multi-dimensional space integrals. Monte Carlo based numerical integration...