Universal Simulation Distributions

Abstract

In the previous chapter, we saw that in the Gaussian setting we could describe completely a sequence of simulation distributions that was efficient and depended on only one scalar parameter, the minimum rate point of the set. In this chapter we consider carrying out these techniques in the general non-Gaussian setting. Due to the special form of the multidimensional Gaussian distribution and its level sets, we could perform a closed form integration of the exponentially shifted distributions over the boundary of the level set. In general, this sort of attack which obtains a closed form solution for the sequence of simulation distributions will not be easily available. In this chapter we present an alternate methodology leading to a new class of simulation distributions, which we call universal distributions. We discuss their use and propose and debate some numerical techniques needed for employing them.

Fate laughs at probabilities.

E. Aram

If I have not seen as far as others, it is because giants were standing on my shoulders.

Anon