Probability Distributions as Program Variables
Dimitrios Milios · 2009
In this work we introduce a new method for performing computations on arbitrarily distributed random variables. Concisely, the probability distributions of input random variables are approximated by mixture models. Computations are then applied to each one of their mixture components. Thus, the final results are also random variables that can be either queried for their density and distribution functions, or even used in future computations. Two alternative types of mixture model approximations have been implemented: mixture of uniforms and mixture of Gaussians. It is remarkable that in some cases, our approach outperformed the equivalent numerical approaches from the literature, in terms of accuracy. The greatest amount of work in this project was spent on the efficiency and accuracy of computations of independent random variables. However, issues of dependencies that are arise in the computations have been studied as well. A way of tracking these dependencies has been developed, although