Monte Carlo and quasi-Monte Carlo probability density estimation for simulation models

21/05/2021, 14:00 - 15:00 in online

Puchhammer, Florian (Basque Center for Applied Mathematics)


Abstract:

Monte Carlo and quasi-Monte Carlo methods are widely used and studied for estimating the expectation of some random model $X$, via several realizations of this model. This data, however, can provide much more information than just the mean and a confidence interval. In fact, it can be used to estimate the entire distribution of $X$. In this talk, we assume that we can generate observations of $X$ by standard Monte Carlo simulation. For that setting, we discuss and compare well known techniques for density estimation (Kernel Density estimators, Histograms) and novel unbiased density estimators based on conditional Monte Carlo and Likelihood Ratio techniques. Moreover, we demonstrate when and how we can apply quasi-Monte Carlo to improve the convergence rate of the mean integrated squared error.

Mathematical Sciences Research Centre