Expected Value of Partial Perfect Information in Hybrid Models Using Dynamic Discretization

Abstract

In decision theory models, expected value of partial perfect information (EVPPI) is an important analysis technique that is used to identify the value of acquiring further information on individual variables. EVPPI can be used to prioritize the parts of a model that should be improved or identify the parts where acquiring additional data or expert knowledge is most beneficial. Calculating EVPPI of continuous variables is challenging, and several sampling and approximation techniques have been proposed. This paper proposes a novel approach for calculating EVPPI in hybrid influence diagram (HID) models (these are influence diagrams (IDs) containing both discrete and continuous nodes). The proposed approach transforms the HID into a hybrid Bayesian network and makes use of the dynamic discretization and the junction tree algorithms to calculate the EVPPI. This is an approximate solution (no feasible exact solution is possible generally for HIDs) but we demonstrate it accurately calculates the EVPPI values. Moreover, unlike the previously proposed simulation-based EVPPI methods, our approach eliminates the requirement of manually determining the sample size and assessing convergence. Hence, it can be used by decision-makers who do not have deep understanding of programming languages and sampling techniques. We compare our approach to the previously proposed techniques based on two case studies.

Keywords

• Bayesian networks
• dynamic discretization
• expected value of partial perfect information
• hybrid influence diagrams
• value of information