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Case Studies in Bayesian Statistical Modelling and Analysis by Anthony N. Pettitt, Kerrie L. Mengersen, Clair L. Alston

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20

Tangled Webs: Using Bayesian Networks in the Fight Against Infection

Mary Waterhouse1,2 and Sandra Johnson1

1Queensland University of Technology, Brisbane, Australia

2Wesley Research Institute, Brisbane, Australia

20.1 Introduction to Bayesian Network Modelling

A Bayesian network (BN) is a probabilistic graphical model showing factors and their interactions, relating to a response of interest (Jensen and Nielsen 2007; Pearl 1988). The graphical model represents factors as nodes, and relationships between factors are shown as directed links which indicate the direction of the dependence between the nodes to form a directed acyclic graph (DAG) (Lauritzen and Sheehan 2003). An example of a DAG is shown in Figure 20.1. The link going from node C4 to node C2 indicates that node C4 is a parent of node C2. Similarly, node C2 is said to be a child of node C4. Apart from the parent–child relationship between two connected nodes, it is possible to distinguish three types of relationships between any three connected nodes in a BN (Korb and Nicholson 2010). These relationship types are serial, converging and diverging and are illustrated in Figure 20.1. The BN characteristics (d-separation and Markov property) inherent in these three relationships are important in their inferencing capabilities and simplification of probability calculations (Koller and Friedman 2009; Korb and Nicholson 2010). The relationships do not need to be causal in nature; however, representing causality in the BN ...

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