Ron S. Kenett (KPA Ltd., Israel)

Applications of Bayesian Networks to Operational Risks, Healthcare, Biotechnology and Customer Surveys

Modelling cause and effect relationships has been a major challenge for statisticians in a wide range of application areas. Bayesian Networks combine graphical analysis with Bayesian analysis to represent descriptive causality maps linking measured and target variables. Such maps can be used for diagnostics and predictive analytics. The talk will present an introduction to Bayesian Networks and their applications to web site usability (Harel et al, Kenett et al, 2009) operational risks (Kenett and Raanan, 2010), biotechnology (Peterson and Kenett, 2011), customer satisfaction surveys (Kenett and Salini, 2011) healthcare systems (Kenett, 2012) and the testing of web services (Bai and Kenett, 2012). Some references to software programs used to construct BNs will be also provided.

Bayesian Networks (BN) implement a graphical model structure known as a directed acyclic graph (DAG) that is popular in Statistics, Machine Learning and Artificial Intelligence. BN are both mathematically rigorous and intuitively understandable. They enable an effective representation and computation of the joint probability distribution over a set of random variables (Pearl, 2000). The structure of a DAG is defined by two sets: the set of nodes and the set of directed edges. The nodes represent random variables and are drawn as circles labeled by the variables names. The edges represent direct dependencies among the variables and are represented by arrows between nodes. In particular, an edge from node Xi to node Xj represents a statistical dependence between the corresponding variables. Thus, an arrow indicates that a value taken by variable Xj depends on the value taken by variable Xi. A BN reflects a simple conditional independence statement, namely that each variable is independent of its non-descendants in the graph given the state of its parents. This property is used to reduce, sometimes significantly, the number of parameters that are required to characterize the joint probability distribution (JPD) of the variables. This reduction provides an efficient way to compute the posterior probabilities given the evidence present in the data (Pearl, 2000, Jensen, 2001, Ben Gal, 2007, Koski and Noble, 2009, Kenett, 2007, 2012). In addition to the DAG structure, which is often considered as the “qualitative” part of the model, one needs to specify the “quantitative” parameters of the model. These parameters are described by applying the Markov property, where the conditional probability distribution (CPD) at each node depends only on its parents. For discrete random variables, this conditional probability is often represented by a table, listing the local probability that a child node takes on each of the feasible values – for each combination of values of its parents. The joint distribution of a collection of variables can be determined uniquely by these local conditional probability tables (CPT). Examples of sensitivity analysis of the BN estimates and the BN structure are provided in Cornalba et al, 2007 and Chapter 11 in Kenett and Salini, 2011.

 References

1. Bai, X., Kenett, R.S. and Yu, W. (2012). Risk Assessment and Adaptive Group Testing of Semantic Web Services. International Journal of Software Engineering and Knowledge Engineering, 2012.

2. Ben Gal, I. (2007). Bayesian Networks, in Encyclopaedia of Statistics in Quality and Reliability, Ruggeri, F., Kenett, R. S. and Faltin, F. (editors in chief), Wiley, UK.

3. Cornalba, C., Kenett, R.S. and Giudici, P. (2007) Sensitivity Analysis of Bayesian Networks with Stochastic Emulators, ENBIS-DEINDE proceedings, University of Torino, Turin, Italy, http://web.econ.unito.it/deinde07/.

4. Jensen, F. V. (2001). Bayesian Networks and Decision Graphs, Springer.

5. Harel. A., Kenett, R.S. and Ruggeri, F. (2009). Modeling Web Usability Diagnostics on the basis of Usage Statistics, in Statistical Methods in eCommerce Research, W. Jank and G. Shmueli (editors), Wiley.

6. Kenett, R.S. (2007). Cause and Effect Diagrams, in Encyclopedia of Statistics in Quality and Reliability, Ruggeri, F., Kenett, R.S. and Faltin, F. (editors in chief), Wiley, Online version, Wiley InterScience, UK.

7. Kenett, R.S., Harel, A. and Ruggeri, F. (2009). Controlling the Usability of Web Services, International Journal of Software Engineering and Knowledge Engineering, Vol. 19, No. 5, pp. 627-651.

8. Kenett R.S. and Salini S. (2009). New Frontiers: Bayesian networks give insight into survey-data analysis, Quality Progress, pp. 31-36, August.

9. Kenett, R.S. and Raanan, Y. (2010). Operational Risk Management: a practical approach to intelligent data analysis, Wiley and Sons. http://www.wiley.com/WileyCDA/WileyTitle/productCd-047074748X.html

10. Kenett R.S. and Salini S. (2011). Modern Analysis of Customer Satisfaction Surveys: with applications using R, John Wiley and Sons, Chichester: UK. http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470971282.html

11. Kenett, R.S. (2012). Risk Analysis in Drug Manufacturing and Healthcare, in Statistical Methods in Healthcare, Faltin, F., Kenett, R.S. and Ruggeri, F. (editors in chief), John Wiley and Sons. 

12. Koski, T. and Noble, J. (2009). Bayesian Networks – An Introduction, John Wiley & Sons, Ltd, West Sussex, UK. 

13. Pearl, J. (2009). Causality: Models, Reasoning, and Inference, 2nd ed., Cambridge University Press, UK. 

14. Peterson, J. and Kenett, R.S. (2011), Modelling Opportunities for Statisticians Supporting Quality by Design Efforts for Pharmaceutical Development and Manufacturing, Biopharmaceutical Report, ASA Publications, Vol. 18, No. 2, pp. 6-16.