Outline:

When simulation is used towards the approximation of a single integral, the reproduction of the underlying distribution is not the primary object of interest and dimension reduction techniques are bound to improve the efficiency of the approximation. Given one or several samples produced towards this approximation, a large range of estimators can be constructed, based on different principles, including some non-parametric versions. The optimal or near-optimal combination of those estimates is mostly an open problem for which Bayesian non-parametric and machine-learning methodologies can help.

 

Themes:

Stochastic simulation, non-parametric density estimation, Bayesian non-parametrics.