Decision making with decision event graphs
Cowell, Robert G., Thwaites, Peter and Smith, J. Q., 1953- (2010) Decision making with decision event graphs. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).
WRAP_cowell_10-15w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
We introduce a new modelling representation, the Decision Event Graph (DEG), for asymmetric multistage decision problems. The DEG explicitly encodes conditional independences and has additional significant advantages over other representations of asymmetric decision problems. The colouring of edges makes it possible to identify conditional independences on decision trees, and these coloured trees serve as a basis for the construction of the DEG. We provide an efficient backward-induction algorithm for finding optimal decision rules on DEGs, and work through an example showing the efficacy of these graphs. Simplifications of the topology of a DEG admit analogues to the sufficiency principle and barren node deletion steps used with influence diagrams.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Statistical decision, Decision trees|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||29|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC)|
|Grant number:||EP/F036752/1 (EPSRC)|
|References:||C. Bielza and P. P. Shenoy. A comparison of graphical techniques for asymmetric decision problems. Management Science, 45(11):1552–1569, 1999. C. Boutilier. The influence of influence diagrams on artificial intelligence. Decision Analysis, 2(4):229–231, 2005. H. J. Call and W. A. Miller. A comparison of approaches and implementations for automating decision analysis. Reliability Engineering and System Safety, 30:115–162, 1990. Z. Covaliu and R. M. Oliver. Representation and solution of decision problems using sequential decision diagrams. Management Science, 41:1860–1881, 1995. R. G. Cowell. Decision networks: a new formulation for multistage decision problems. Research Report 132, Department of Statistical Science, University College London, London, United Kingdon, 1994. R. G. Cowell, A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter. Probabilistic Networks and Expert Systems. Springer, New York, 1999. A. P. Dawid. Separoids: A mathematical framework for conditional independence and irrelevance. Annals of Mathematics and Artificial Intelligence, 32:335–372, 2001. R. A. Howard and J. E. Matheson. Influence diagrams. In R. A. Howard and J. E. Matheson, editors, Readings in the Principles and Applications of Decision Analysis. Strategic Decisions Group, Menlo Park, California, 1984. R. A. Howard and J. E. Matheson. Influence diagram retrospective. Decision Analysis, 2(3):144–147, 2005. F. Jensen, F. V. Jensen, and S. L. Dittmer. From influence diagrams to junction trees. In R. L. de Mantaras and D. Poole, editors, Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence, pages 367–373, San Francisco, California, 1994. Morgan Kaufmann. F. V. Jensen and T. D. Nielsen. Bayesian networks and decision graphs. Springer, 2007. 2nd edition. R. L. Keeney and H. Raiffa. Decisions with multiple objectives: Preferences and Value trade-offs. Wiley, New York, 1976. D. V. Lindley. Making Decisions. John Wiley and Sons, Chichester, United Kingdom, 1985. S. M. Olmsted. On Representing and Solving Decision Problems. Ph.D. Thesis, Department of Engineering– Economic Systems, Stanford University, Stanford, California, 1983. J. Pearl. Influence diagrams—historical and personal perspectives. Decision Analysis, 2(4):232–234, 2005. H. Raiffa. Decision Analysis. Addison–Wesley, Reading, Massachusetts, 1968. H. Raiffa and R. Schlaifer. Applied Statistical Decision Theory. MIT Press, Cambridge, Massachusetts, 1961. R. D. Shachter. Evaluating influence diagrams. Operations Research, 34:871–882, 1986. P. P. Shenoy. Representing and solving asymmetric decision problems using valuation networks. In D. Fisher and H.-J. Lenz, editors, Learning from Data: Artificial Intelligence and Statistics V, pages 99–108. Springer–Verlag, New York, 1996. J. E. Smith and S. H. J. E. Matheson. Structuring conditional relationships in influence diagrams. Operations Research, 41(2):280–297, 1993. J. Q. Smith. Bayesian Decision Analysis: Principles and Practice. CUP, 2010. (to appear). J. Q. Smith. Influence diagrams for Bayesian decision analysis. European Journal of Operational Research, 40:363–376, 1989a. J. Q. Smith. Influence diagrams for statistical modelling. Annals of Statistics, 7:654–672, 1989b. J. Q. Smith. Plausible Bayesian Games. In J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics 5, pages 387–402. Oxford, 1996. J. Q. Smith and P. E. Anderson. Conditional independence and chain event graphs. Artificial Intelligence, 172:42–68, 2008. J. Q. Smith and P. A. Thwaites. Decision trees. In Encyclopedia of Quantitative Risk Analysis and assessment, volume 2, pages 462–470. Wiley, 2008a. J. Q. Smith and P. A. Thwaites. Influence diagrams. In Encyclopedia of Quantitative Risk Analysis and assessment, volume 2, pages 897–909. Wiley, 2008b. J. Q. Smith, E. Riccomagno, and P. Thwaites. Causal analysis with chain event graphs. Submitted to Artificial Intelligence, 2009. P. Thwaites, J. Q. Smith, and R. G. Cowell. Propagation using chain event graphs. In D. McAllester and P. Myllym¨aki, editors, Proceedings of the 24th Conference in Uncertainty in Artificial Intelligence, Helsinki, July 2008, pages 546–553, 2008.|
Actions (login required)