Freeman, Guy and Smith, J. Q., 1953- (2010) Dynamic staged trees for discrete multivariate time series : forecasting, model selection and causal analysis. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

Preview

PDF WRAP_Freeman_10-14w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (484Kb)

Abstract

A new tree-based graphical model — the dynamic staged tree — is used to model discrete-valued discrete-time multivariate processes which are hypothesised to exhibit certain symmetries concerning how situations might unfold. We define and implement a one-step-ahead prediction algorithm using multi-process modelling and the power steady model. This is robust to short-term variations in the data yet sensitive to underlying system changes. We demonstrate that the whole analysis can be performed in a conjugate way so that the vast model space can be traversed quickly and results communicated transparently. We also demonstrate how to analyse causal hypotheses on this model class. Our techniques are illustrated using a simple educational example.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Time-series analysis, Graphical modeling (Statistics), Trees (Graph theory)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2010
Volume:	Vol.2010
Number:	No.14
Number of Pages:	22
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Arjas, E. (1989). Survival models and martingale dynamics (with discussion and reply). Scandinavian Journal of Statistics 16(3), 177–225. ArticleType: primary_article / Full publication date: 1989 / Copyright © 1989 Board of the Foundation of the Scandinavian Journal of Statistics. Boutilier, C., N. Friedman, M. Goldszmidt, and D. Koller (1996). Context-Specific independence in bayesian networks. In Uncertainty in Artificial Intelligence, pp. 115–123. Cooper, G. and C. Yoo (1999). Causal discovery from a mixture of experimental and observational data. In Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence (UAI-99), San Francisco, CA, pp. 116–12. Morgan Kaufmann. Cowell, R. G., A. P. Dawid, S. L. Lauritzen, and D. J. Spiegelhalter (1999). Probabilistic Networks and Expert Systems. Springer. Dawid, A. P. (1979). Conditional independence in statistical theory. Journal of the Royal Statistical Society. Series B (Methodological) 41(1), 1–31. Dawid, A. P. (1984). Present position and potential developments: Some personal views: Statistical theory: The prequential approach. Journal of the Royal Statistical Society. Series A (General) 147(2), 278–292. ArticleType: primary_article / Issue Title: The 150th Anniversary of the Royal Statistical Society / Full publication date: 1984 / Copyright © 1984 Royal Statistical Society. Didelez, V. (2008, February). Graphical models for marked point processes based on local independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 70(1), 245–264. Eichler, M. and V. Didelez (2007). Causal reasoning in graphical time series models. In Proceedings of the 23rd Annual Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann Publishers. Freeman, G. and J. Q. Smith (2009). Bayesian MAP model selection of chain event graphs. CRiSM 09-06, University of Warwick, Coventry. Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York: Springer. Gottard, A. (2007, November). On the inclusion of bivariate marked point processes in graphical models. Metrika 66(3), 269–287. Harrison, P. J. and C. F. Stevens (1976). Bayesian forecasting. Journal of the Royal Statistical Society. Series B (Methodological) 38(3), 205–247. ArticleType: primary_article / Full publication date: 1976 / Copyright © 1976 Royal Statistical Society. Heckerman, D. (1999). A tutorial on learning with Bayesian networks. In M. I. Jordan (Ed.), Learning in Graphical Models, pp. 301–354. MIT Press. Ibrahim, J. G. and M. Chen (2000, February). Power prior distributions for regression models. Statistical Science 15(1), 46–60. ArticleType: primary_article / Full publication date: Feb., 2000 / Copyright © 2000 Institute of Mathematical Statistics. Kullback, S. and R. A. Leibler (1951, March). On information and sufficiency. The Annals of Mathematical Statistics 22(1), 79–86. ArticleType: primary_article / Full publication date: Mar., 1951 / Copyright © 1951 Institute of Mathematical Statistics. Madigan, D. and A. E. Raftery (1994, December). Model selection and accounting for model uncertainty in graphical models using Occam’s window. Journal of the American Statistical Association 89(428), 1535–1546. ArticleType: primary_article / Full publication date: Dec., 1994 / Copyright © 1994 American Statistical Association. Meilă, M. (2007, May). Comparing clusterings–an information based distance. Journal of Multivariate Analysis 98(5), 873–895. Pearl, J. (2000a, June). Causal inference without counterfactuals: Comment. Journal of the American Statistical Association 95(450), 428–431. ArticleType: primary_article / Full publication date: Jun., 2000 / Copyright © 2000 American Statistical Association. Pearl, J. (2000b). Causality. Cambridge University Press. Queen, C. M. and C. J. Albers (2009, June). Intervention and causality: Forecasting traffic flows using a dynamic bayesian network. Journal of the American Statistical Association 104(486), 669–681. Queen, C. M. and J. Q. Smith (1993). Multiregression dynamic models. Journal of the Royal Statistical Society. Series B (Methodological) 55(4), 849–870. Queen, C. M., J. Q. Smith, and D. M. James (1994, September). Bayesian forecasts in markets with overlapping structures. International Journal of Forecasting 10(2), 209–233. Raftery, A. E., M. Kárný, and P. Ettler (2010). Online prediction under model uncertainty via dynamic model averaging: Application to a cold rolling mill. Technometrics 52(1), 52–66. Rigat, F. and J. Q. Smith (2009). Semi-parametric dynamic time series modelling with applications to detecting neural dynamics. The Annals of Applied Statistics 3(4), 1776–1804. Shafer, G. (1996, November). The Art of Causal Conjecture. Artificial Intelligence. The MIT Press. Smith, J. Q. (1979). A generalization of the bayesian steady forecasting model. Journal of the Royal Statistical Society. Series B (Methodological) 41(3), 375–387. Smith, J. Q. (1981). The multiparameter steady model. Journal of the Royal Statistical Society. Series B (Methodological) 43(2), 256–260. Smith, J. Q. (1992, April). A comparison of the characteristics of some bayesian forecasting models. International Statistical Review 60(1), 75–87. Smith, J. Q. and P. E. Anderson (2008, January). Conditional independence and chain event graphs. Artificial Intelligence 172(1), 42–68. Smith, J. Q. and A. Daneshkhah (2010, June). On the robustness of bayesian networks to learning from non-conjugate sampling. International Journal of Approximate Reasoning 51(5), 558–572. Smith, J. Q. and F. Rigat (2008). Isoseparation and robustness in finite parameter Bayesian inference. CRiSM 07-22, University of Warwick, Coventry. Spirtes, P., C. N. Glymour, and R. Scheines (2001). Causation, Prediction, and Search (2nd ed.). MIT Press. Stanley, R. (1997). Enumerative combinatorics. Cambridge: Cambridge University Press. Studený, M. (2005). Probabilistic conditional independence structures. Information Science and Statistics. London: Springer. Thwaites, P., J. Q. Smith, and E. Riccomagno (2010, August). Causal analysis with chain event graphs. Artificial Intelligence 174(12-13), 889–909. Thwaites, P. E. and J. Q. Smith (2006, September). Evaluating causal effects using chain event graphs. In Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, Prague. West, M. and J. Harrison (1989). Subjective intervention in formal models. Journal of Forecasting 8(1), 33–53. West, M. and J. Harrison (1997, February). Bayesian Forecasting and Dynamic Models (Second ed.). Springer Series in Statistics. Springer-Verlag.
URI:	http://wrap.warwick.ac.uk/id/eprint/35107

Request changes to a record

Actions (login required)

View Item