Another look at sensitivity of Bayesian networks to imprecise probabilities

Oscar Kipersztok, Haiqin Wang
Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, PMLR R3:149-155, 2001.

Abstract

Empirical study of sensitivity analysis on a Bayesian network examines the effects of varying the network’s probability parameters on the posterior probabilities of the true hypothesis. One appealing approach to modeling the uncertainty of the probability parameters is to add normal noise to the log-odds of the nominal probabilities. However, the paper argues that differences in sensitivities found on true hypothesis may only be valid in the range of standard deviations where the log-odds normal distribution is unimodal. The paper also shows that using average posterior probabilities as criterion to measure the sensitivity may not be the most indicative, especially when the distribution is very asymmetric as is the case at nominal values close to zero or one. It is proposed, instead, to use the partial ordering of the most probable causes of diagnosis, measured by a suitable lower confidence bound. The paper also presents the preliminary results of our sensitivity analysis experiments with three Bayesian networks built for diagnosis of airplane systems. Our results show that some networks are more sensitive to imprecision in probabilities than previously believed.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR3-kipersztok01a, title = {Another look at sensitivity of Bayesian networks to imprecise probabilities}, author = {Kipersztok, Oscar and Wang, Haiqin}, booktitle = {Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics}, pages = {149--155}, year = {2001}, editor = {Richardson, Thomas S. and Jaakkola, Tommi S.}, volume = {R3}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r3/kipersztok01a/kipersztok01a.pdf}, url = {https://proceedings.mlr.press/r3/kipersztok01a.html}, abstract = {Empirical study of sensitivity analysis on a Bayesian network examines the effects of varying the network’s probability parameters on the posterior probabilities of the true hypothesis. One appealing approach to modeling the uncertainty of the probability parameters is to add normal noise to the log-odds of the nominal probabilities. However, the paper argues that differences in sensitivities found on true hypothesis may only be valid in the range of standard deviations where the log-odds normal distribution is unimodal. The paper also shows that using average posterior probabilities as criterion to measure the sensitivity may not be the most indicative, especially when the distribution is very asymmetric as is the case at nominal values close to zero or one. It is proposed, instead, to use the partial ordering of the most probable causes of diagnosis, measured by a suitable lower confidence bound. The paper also presents the preliminary results of our sensitivity analysis experiments with three Bayesian networks built for diagnosis of airplane systems. Our results show that some networks are more sensitive to imprecision in probabilities than previously believed.}, note = {Reissued by PMLR on 31 March 2021.} }
Endnote
%0 Conference Paper %T Another look at sensitivity of Bayesian networks to imprecise probabilities %A Oscar Kipersztok %A Haiqin Wang %B Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2001 %E Thomas S. Richardson %E Tommi S. Jaakkola %F pmlr-vR3-kipersztok01a %I PMLR %P 149--155 %U https://proceedings.mlr.press/r3/kipersztok01a.html %V R3 %X Empirical study of sensitivity analysis on a Bayesian network examines the effects of varying the network’s probability parameters on the posterior probabilities of the true hypothesis. One appealing approach to modeling the uncertainty of the probability parameters is to add normal noise to the log-odds of the nominal probabilities. However, the paper argues that differences in sensitivities found on true hypothesis may only be valid in the range of standard deviations where the log-odds normal distribution is unimodal. The paper also shows that using average posterior probabilities as criterion to measure the sensitivity may not be the most indicative, especially when the distribution is very asymmetric as is the case at nominal values close to zero or one. It is proposed, instead, to use the partial ordering of the most probable causes of diagnosis, measured by a suitable lower confidence bound. The paper also presents the preliminary results of our sensitivity analysis experiments with three Bayesian networks built for diagnosis of airplane systems. Our results show that some networks are more sensitive to imprecision in probabilities than previously believed. %Z Reissued by PMLR on 31 March 2021.
APA
Kipersztok, O. & Wang, H.. (2001). Another look at sensitivity of Bayesian networks to imprecise probabilities. Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R3:149-155 Available from https://proceedings.mlr.press/r3/kipersztok01a.html. Reissued by PMLR on 31 March 2021.

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