Biasing in random number space

Abstract

An interesting way to compare the biased random number technique to more conventional biasing techniques is to consider what is really calculated by analog Monte-Carlo. Each history is associated with a random number sequence \(\vec r_i\) and a history score \(T(\vec r_i )\) that depends on the random walk specified by \(\vec r_i\). The random number sequence \(\vec r_i\) is selected from a uniform density \(f(\vec r)\) of random number sequences. The expected score is then: $$E = \smallint T(\vec r)f(\vec r)d\vec r$$ .