This work deals with the propagation of uncertainty in decision analysis problems. In the practice, the distribution of the decision support model output (O) is obtained numerically by means of subroutines implemented on standard decision support software. We undertake the analytical calculations of the moments of O when the model is expressed in the form of an influence diagram or decision tree. Our purpose is that of providing an analytical background to calculations which are usually performed numerically. After providing the expression of the generic central and noncentral moment of O, we prove that the expected value of O equals the weighted average of the utility of all the consequences. The discussion of the meaning of the weights enables us to generalize risk profile diagrams to the case in which uncertainty in the probabilities is considered. We next derive expression of the variance of O as a function of the uncertain parameters. We illustrate the above mentioned results in detail by analyzing a simple decision-making problem. The application to the prior and posterior analysis of an industrial investment case study concludes the work.

Uncertainty Propagation in Decision Support Models

BORGONOVO, EMANUELE
2009

Abstract

This work deals with the propagation of uncertainty in decision analysis problems. In the practice, the distribution of the decision support model output (O) is obtained numerically by means of subroutines implemented on standard decision support software. We undertake the analytical calculations of the moments of O when the model is expressed in the form of an influence diagram or decision tree. Our purpose is that of providing an analytical background to calculations which are usually performed numerically. After providing the expression of the generic central and noncentral moment of O, we prove that the expected value of O equals the weighted average of the utility of all the consequences. The discussion of the meaning of the weights enables us to generalize risk profile diagrams to the case in which uncertainty in the probabilities is considered. We next derive expression of the variance of O as a function of the uncertain parameters. We illustrate the above mentioned results in detail by analyzing a simple decision-making problem. The application to the prior and posterior analysis of an industrial investment case study concludes the work.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11565/40075
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? ND
social impact