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Monte Carlo Integration

AMonte Carlo IntegrationTHE techniques developed in this dissertation are all Monte Carlo methods. Monte Carlomethods are numerical techniques which rely on random sampling toapproximatetheirresults. Monte Carlo Integration applies this process to the numerical estimation of integrals. Inthis appendix we review the fundamental concepts of Monte Carlo Integration upon which ourmethods are based. From this discussion we will see why Monte Carlo methods are a particularlyattractive choice for the multidimensional Integration problems common in computer references for Monte Carlo Integration in the context of computer graphics include Pharrand Humphreys [2004], Dutr et al.

R). In computer graphics we more commonly deal with continuous random variables which take on values over ranges of continuous domains (e.g., the real numbers R or the sphere of directions ›). A.1.2 Cumulative Distributions and Density Functions The cumulative distribution function, or CDF, of a random variable X is the probability

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  Integration, Oracl, Monte, Monte carlo integration

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