Continuous trees and NEVADA simulation: a quadrature approach to modeling continuous random variables in decision analysis.

Abstract

This paper introduces an improved technique for modeling risk and decision problems that have continuous random variables and probabilistic dependence. Variables are modeled with mixtures of four-parameter random variables, called "continuous trees." Functions of random variables are calculated using gaussian quadrature in a manner called "Nevada simulation" (NumErical Integration of Variance And probabilistic Dependence Analyzer). This technique is compared with traditional decision-tree modeling in terms of analytic technique, solution-time complexity, and accuracy. Nevada simulation takes advantage of the probabilistic independence in a decision problem while allowing for probabilistic dependence to achieve polynomial computational-time complexity for many decision problems. It improves on the accuracy of traditional decision trees by employing larger approximations than traditional decision analysis. It improves on traditional decision analysis by modeling continuous variables with continuous, rather than discrete, distributions. A Bayesian analysis using a mixed discrete-continuous probability distribution for cigarette smoking rate is presented.