Bayesian belief network framework

Figure 7.1. A causal graph for risk analysis. The model depicted in this figure can be formalized using a Bayesian network (Ricci et al. 2006) A probabilistic framework interprets the model described in this figure as a Bayesian belief network or causal graph model. Each variable with inward-pointing arrows is interpreted as a random variable with a conditional probability distribution that depends only on the values of the variables that point into it. The essence of this approach to modeling and evaluating uncertain risks is to sample successively from the (often conditional) distribution of each variable, given the values of its predecessors. Algorithms exist to identify and validate possible causal structures.

The proposed model consists of two components a system d3mamics framework and a Bayesian belief network structure. The system dynamics formalism enables us to represent change over time and change due to feedback. The Bayesian behef network formalism enables us to represent networks of causality and capture stocasticity and uncertainty. BBNs also enable us to incorporate new knowledge and update the model as new evidence becomes available. Combining SD and BBN has been previously proposed and applied in aviation risk context (Mohaghegb, et.al., 2008). 

Current approaches to model risk in healthcare that have been borrowed from engineering domain and industry, have not proven to be effective and insight-fid, for a niunber of specific reasons. Unlike industry, in healthcare, there is much more variability in the procedures. Traditional PRA methods assinne a linear chain of independent events that lead to an accident or an unsafe condition, which by far is not the case in healthcare. Much of what happens in healthcare is subject to feedbacks. A hybrid approach to modeling risk in healthcare settings, as a combination of two modeling formalisms (system dynamics and Bayesian belief networks), has been proposed. We beheve that the proposed framework overcomes the deficiencies of conventional engineering risk analysis methods by its capability to explicitly model the feedback loops, time delays and the nonlinearities that exist in a complex healthcare setting. 

ABSTRACT Dependencies or failure dependencies in probabilistic risk assessments may lead to significant errors if not properly analyzed. In order to overcome the limitations of tradition methods, a modified Bayesian Network (BN), which is called Evidential Network (EN), was proposed with evidence theory to handle dependencies in Probabilistic Risk Assessment (PRA). Fault Trees (IT s) and Event Trees (ETs) were transformed into an EN which constructs a uniform framework to represent accident scenarios. Dependencies can be processed through the corresponding evidential networks where uncertainties are characterized by basic belief mass. A case study was discussed to demonstrate the proposed approach. Frequencies of end states were obtained and expressed by belief and plausibility measures. The proposed approach can be easily applied to probabilistic risk assessments that involve dependencies while addresses the uncertainties in experts knowledge. 

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