LOCAL ROBUSTNESS ANALYSIS IN JAVABAYES

 

In this section we describe an implementation of local robust analysis for Quasi-Bayesian networks and present an example to illustrate the methods.

Local robust analysis is available in the JavaBayes system, a portable and freely distributed inference engine for graphical models. JavaBayes is written in Java and can run in any computing platform that supports the Java virtual machine. JavaBayes uses standard algorithms to perform calculation of posterior marginals, expectations, maximum a posteriori explanations and maximum a posteriori expectation. Documentation, code and examples for JavaBayes can be downloaded from http://www.cs.cmu.edu/~fgcozman/Research/JavaBayes/Home.

As an example, consider a troubleshooting problem where the objective is to analyze the state of a car [20], which contains 17 variables and several deterministic and stochastic relationships. Suppose there is some imprecision in the probability values for two variables. First, take the variable BatteryAge, which has two values, Old and New. Suppose this variable is associated with an epsi-contaminated credal set where epsi= 0.2 and p(BatteryAge) = (0.75, 0.25) (as detailed in the Appendix). We conclude that this variable is associated with a polytopic credal set with vertices (0.8, 0.2) and (0.6, 0.4). Second, take the binary variable Lights, which depends on the binary variable BatteryPower. Suppose the expert defines the conditional distribution depicted in Table 1.

 

BatteryPower rarr Good Poor

Lights = Work 0.8 0

Lights = NoLight 0.2 1

BatteryPower rarr Good Poor

Lights = Work 0.944444 0

Lights = NoLight 0.055555 1

 

This model can be inserted into JavaBayes together with arbitrary evidence. For example, if the variable Starts is set to No, the posterior lower bounds for the binary variable BatteryPower are (0.7037, 0.2702) and the posterior upper bounds are (0.7297, 0.2963).