Questions tagged [monte-carlo]

So I was reading this paper by Lafortune, "Mathematical Models and Monte Carlo algorithms" and in it he writes. We have a function or integrand I we want to estimate given as, $I = \int f(x) dx$ We then have a primary estimator for this…

I cannot understand an algorithm which combines stratified sampling and importance sampling of Monte Carlo. It is introduced in Page 73 of a textbook "Advanced Global Illumination", 2nd edition, written by Philip Dutre, Philippe Bekaert and Kavita…

In the Monte Carlo chapter of PBRT, in the section Transforming Between Distributions, they say "The density with respect to $\theta$ and $\phi$ can therefore be derived", but they start with \begin{align} p(\theta, \phi) \ d\theta \ d\phi =…

I am trying to prove the equality of $$\rm MSE(\langle I\rangle)=Var(\langle I \rangle)+Bias(\langle I \rangle)^2$$ but obviously I got something wrong as they don't equal in my calculation: So here is the example. I use monte carlo to estimate this…