Revisiting the balance heuristic for estimating normalising constants

Understand

Multiple importance sampling estimators are widely used for computing intractable constants due to its reliability and robustness.

• The celebrated balance heuristic estimator belongs to this class of methods and has proved very successful in computer graphics.
• The basic ingredients for computing the estimator are: a set of proposal distributions, indexed by some discrete label, and a predetermined number of draws from each of these proposals.
• However, if the number of available proposals is much larger than the number of permitted importance points, one needs to select, possibly at random, which of these distributions will be used.