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Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach

Abstract : Ensuring the validity and credibility of Bayesian Belief Network (BBN) as a modelling tool for expert systems requires appropriate methods for sensitivity analysis (SA), in order to test the robustness of the BBN diagnostic and prognostic with respect to the parameterisation of the conditional probability model (CPM). Yet, the most widely used techniques (based on sensitivity functions for discrete BBNs) only provide a local insight on the CPM influence, i.e. by varying only one CPM parameter at a time (or a few of them) while keeping the other ones unchanged. To overcome this limitation, the present study proposes an approach for global SA relying on Beta Regression using gradient boosting (potentially combined with stability selection analysis): it presents the benefit of keeping the presentation intuitive through a graph-based approach, while being applicable to a large number of CPM parameters. The implementation of this approach is investigated for three cases, which cover a large spectrum of situations: (1) a small discrete BBN, used to capture medical knowledge, demonstrates the proposed approach; (2) a linear Gaussian BBN, used to assess the damage of reinforced concrete structures, exemplifies a case where the number of parameters is too large to be easily processed and interpreted (>40 parameters); (3) a discrete BBN, used for reliability analysis of nuclear power plant, exemplifies a case where analytical solutions for sensitivity can hardly be derived. Finally, provided that the validity of the BBR model is carefully checked, we show that the proposed approach can provide richer information than traditional SA methods at different levels: (i) it selects the most influential parameters; (ii) it provides the functional relation between the CPM parameter and the result of the probabilistic query; and (iii) it identifies how the CPM parameters can lead to situations of high probability, while quantifying the confidence in the occurrence of these situations.
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Soumis le : jeudi 12 décembre 2019 - 17:15:05
Dernière modification le : mardi 31 mars 2020 - 10:46:02
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  • HAL Id : hal-02408006, version 1

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Jeremy Rohmer, Pierre Gehl. Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach. Expert Systems with Applications, Elsevier, In press. ⟨hal-02408006⟩

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