Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective - Archive ouverte HAL Access content directly
Reports (Research Report) Year : 2015

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

Abstract

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. 2 Problem Statmement We begin by reviewing some basic concepts from Monte Carlo integration. Next, we present a formal definition of homogeneity. And finally, we formulate the generalized problem statement.
Fichier principal
Vignette du fichier
1506.00021v1.pdf (88.35 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01259838 , version 1 (21-01-2016)

Identifiers

Cite

Michael Kazhdan, Gurprit Singh, Adrien Pilleboue, David Coeurjolly, Victor Ostromoukhov. Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective. [Research Report] LIRIS UMR CNRS 5205. 2015. ⟨hal-01259838⟩
195 View
101 Download

Altmetric

Share

Gmail Facebook X LinkedIn More