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Dynamic staged trees for discrete multivariate time series : forecasting, model selection and causal analysis

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Freeman, Guy and Smith, J. Q., 1953-. (2011) Dynamic staged trees for discrete multivariate time series : forecasting, model selection and causal analysis. Bayesian Analysis, Vol.6 (No.2). pp. 279-306. ISSN 1931-6690

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Official URL: http://dx.doi.org/10.1214/11-BA610

Abstract

A new tree-based graphical model the dynamic staged tree is proposed for modelling discrete-valued discrete-time multivariate processes which are hypothesised to exhibit symmetries in how some intermediate situations might unfold. We define and implement a one-step-ahead prediction algorithm with the model using multi-process modelling and the power steady model that 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 potentially vast model space can be traversed quickly and then results communicated transparently. We also demonstrate how to analyse a general set of causal hypotheses on this model class. Our techniques are illustrated using a simple educational example.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Time-series analysis, Trees (Graph theory), Multivariate analysis
Journal or Publication Title:	Bayesian Analysis
Publisher:	International Society for Bayesian Analysis
ISSN:	1931-6690
Date:	2011
Volume:	Vol.6
Number:	No.2
Page Range:	pp. 279-306
Identification Number:	10.1214/11-BA610
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	EP/F036752/1 (EPSRC)
References:	Arjas, E. (1989). \Survival Models and Martingale Dynamics (with Discussion and Reply)." Scandinavian Journal of Statistics, 16(3): 177{225. ArticleType: pri- mary article / Full publication date: 1989 / Copyright © 1989 Board of the Foun- dation of the Scandinavian Journal of Statistics. URL http://www.jstor.org/stable/4616135 301 Boutilier, C., Friedman, N., Goldszmidt, M., and Koller, D. (1996). \Context-Speci¯c Independence in Bayesian Networks." In Horvitz, E. and Jensen, F. V. (eds.), Pro- ceedings of the Twelfth Conference on Uncertainty in Arti¯cial Intelligence, 115{123. Reed College, Portland, Oregon, USA: Morgan Kaufmann. URL http://citeseer.ist.psu.edu/4780.html 282 Cooper, G. and Yoo, C. (1999). \Causal Discovery from a Mixture of Experimental and Observational Data." In Proceedings of the 15th Annual Conference on Uncertainty in Arti¯cial Intelligence (UAI-99), 116{12. San Francisco, CA: Morgan Kaufmann. 294 Cowell, R. G., Dawid, A. P., Lauritzen, S. L., and Spiegelhalter, D. J. (2007). Proba- bilistic Networks and Expert Systems. Springer. 281, 290 Dawid, A. P. (1979). \Conditional Independence in Statistical Theory." Journal of the Royal Statistical Society. Series B (Methodological), 41(1): 1{31. URL http://www.jstor.org/stable/2984718 281 \| (1984). \Present Position and Potential Developments: Some Personal Views: Sta- tistical 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. URL http://www.jstor.org/stable/2981683 285 Didelez, V. (2008). \Graphical models for marked point processes based on local inde- pendence." Journal of the Royal Statistical Society: Series B (Statistical Methodol- ogy), 70(1): 245{264. URL http://dx.doi.org/10.1111/j.1467-9868.2007.00634.x 301 Eichler, M. and Didelez, V. (2007). \Causal reasoning in graphical time series models." In Proceedings of the 23rd Annual Conference on Uncertainty in Arti¯cial Intelligence. Morgan Kaufmann Publishers. URL http://arno.unimaas.nl/show.cgi?did=13833 294 Freeman, G. and Smith, J. Q. (2011). \Bayesian MAP model selection of chain event graphs." Journal of Multivariate Analysis, In Press, doi:10.1016/j.jmva.2011.03.008. URL http://www.sciencedirect.com/science/article/B6WK9-52GNCYY-3/2/ 0d6dad79883d7817d599225d2faae13f 283, 287 FrÄuhwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. New York: Springer. 282 Geiger, D. and Heckerman, D. (1996). \Knowledge representation and inference in similarity networks and Bayesian multinets." Arti¯cial Intelligence, 82(1-2): 45{74. URL http://www.sciencedirect.com/science/article/B6TYF-3VS5GXF-3/2/ ade85e0fd7d2d91772b01ec4078c22fd 282 Gottard, A. (2007). \On the inclusion of bivariate marked point processes in graphical models." Metrika, 66(3): 269{287. URL http://dx.doi.org/10.1007/s00184-006-0110-7 301 Harrison, P. J. and Stevens, C. F. (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. URL http://0-www.jstor.org.pugwash.lib.warwick.ac.uk/stable/2984970 282, 290 Heckerman, D. (1999). \A tutorial on learning with Bayesian networks." In Jordan, M. I. (ed.), Learning in Graphical Models, 301{354. MIT Press. 287 Ibrahim, J. G. and Chen, M. (2000). \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. URL http://0-www.jstor.org.pugwash.lib.warwick.ac.uk/stable/2676676 290 Kullback, S. and Leibler, R. A. (1951). \On Information and Su±ciency." The Annals of Mathematical Statistics, 22(1): 79{86. ArticleType: primary article / Full publi- cation date: Mar., 1951 / Copyright © 1951 Institute of Mathematical Statistics. URL http://www.jstor.org/stable/2236703 289 Madigan, D. and Raftery, A. E. (1994). \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 pub- lication date: Dec., 1994 / Copyright © 1994 American Statistical Association. URL http://www.jstor.org/stable/2291017 293 Meil¸a, M. (2007). \Comparing clusterings{an information based distance." Journal of Multivariate Analysis, 98(5): 873{895. URL http://0-www.sciencedirect.com.pugwash.lib.warwick.ac.uk/science/ article/B6WK9-4MMWHFV-1/2/6e6d4d7733be150b256bcd50a651c241 291 Pearl, J. (2000). Causality. Cambridge University Press. 281, 283, 294, 295 Queen, C. M. and Albers, C. J. (2009). \Intervention and Causality: Forecasting Tra±c Flows Using a Dynamic Bayesian Network." Journal of the American Statistical Association, 104(486): 669{681. URL http://stats-www.open.ac.uk/TechnicalReports/QueenAlbers.pdf 294 Queen, C. M. and Smith, J. Q. (1993). \Multiregression Dynamic Models." Journal of the Royal Statistical Society. Series B (Methodological), 55(4): 849{870. URL http://www.jstor.org/stable/2345998 294 Queen, C. M., Smith, J. Q., and James, D. M. (1994). \Bayesian forecasts in markets with overlapping structures." International Journal of Forecasting, 10(2): 209{233. URL http://0-www.sciencedirect.com.pugwash.lib.warwick.ac.uk/science/ article/B6V92-45MGSV6-1M/2/becf223a480542044b19ea7ac51a9587 290 Raftery, A. E., K¶arn¶y, M., and Ettler, P. (2010). \Online Prediction Under Model Uncertainty via Dynamic Model Averaging: Application to a Cold Rolling Mill." Technometrics, 52(1): 52{66. URL http://pubs.amstat.org/doi/abs/10.1198/TECH.2009.08104 290 Rigat, F. and Smith, J. Q. (2009). \Semi-parametric dynamic time series modelling with applications to detecting neural dynamics." The Annals of Applied Statistics, 3(4): 1776{1804. URL http://projecteuclid.org/euclid.aoas/1267453964 290 Shafer, G. (1996). The Art of Causal Conjecture. Arti¯cial Intelligence. The MIT Press. URL http://www.amazon.ca/exec/obidos/redirect?tag=citeulike09-20& path=ASIN/026219368X 280, 283, 294 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. URL http://www.jstor.org/stable/2985066 282, 288, 290 \|(1981). \The Multiparameter Steady Model." Journal of the Royal Statistical Society. Series B (Methodological), 43(2): 256{260. URL http://www.jstor.org/stable/2984856 288 \| (1992). \A Comparison of the Characteristics of Some Bayesian Forecasting Models." International Statistical Review / Revue Internationale de Statistique, 60(1): 75{87. ArticleType: primary article / Full publication date: Apr., 1992 / Copyright © 1992 International Statistical Institute (ISI). URL http://0-www.jstor.org.pugwash.lib.warwick.ac.uk/stable/1403502 282, 288 Smith, J. Q. and Anderson, P. E. (2008). \Conditional independence and chain event graphs." Arti¯cial Intelligence, 172(1): 42{68. URL http://dx.doi.org/10.1016/j.artint.2007.05.004 280, 282, 283, 284 Smith, J. Q. and Daneshkhah, A. (2010). \On the robustness of Bayesian networks to learning from non-conjugate sampling." International Journal of Approximate Reasoning, 51(5): 558{572. URL http://www.sciencedirect.com/science/article/B6V07-4Y88D9H-5/2/ 62e672471ab099938ee27eece654ea68 289 Smith, J. Q. and Rigat, F. (2008). \Isoseparation and Robustness in Finite Parameter Bayesian Inference." CRiSM 07-22, University of Warwick, Coventry. URL http://www2.warwick.ac.uk/fac/sci/statistics/crism/research/2007/ paper07-22 289 Spirtes, P., Glymour, C. N., and Scheines, R. (2001). Causation, Prediction, and Search. MIT Press, 2nd edition. 294 Stanley, R. (1997). Enumerative combinatorics. Cambridge: Cambridge University Press. 291 Studen, M. (2005). Probabilistic conditional independence structures. Information Science and Statistics. London: Springer. 281 Thwaites, P., Smith, J. Q., and Riccomagno, E. (2010). \Causal analysis with Chain Event Graphs." Arti¯cial Intelligence, 174(12-13): 889{909. URL http://www.sciencedirect.com/science/article/B6TYF-5046MC2-1/2/ 3728ca449be680c0ae809f0aec5542d9 283, 294 Thwaites, P. A., Freeman, G., and Smith, J. Q. (2009). \Chain Event Graph Map Model Selection." In Dietz, J. L. G. (ed.), Proceedings of the International Conference on Knowledge Engineering and Ontology Development, 392{395. Funchal, Madeira, Portugal: INSTICC Press. 280 Thwaites, P. E. and Smith, J. Q. (2006). \Evaluating Causal e®ects using Chain Event Graphs." In Proceedings of the 3rd European Workshop on Probabilistic Graphical Models. Prague. 294 West, M. and Harrison, J. (1989). \Subjective intervention in formal models." Journal of Forecasting, 8(1): 33{53. URL http://dx.doi.org/10.1002/for.3980080104 294 \| (1997). Bayesian Forecasting and Dynamic Models. Springer Series in Statistics. Springer-Verlag, second edition. Published: Hardcover. URL http://www.amazon.ca/exec/ob
URI:	http://wrap.warwick.ac.uk/id/eprint/40061