Compatible prior distributions for directed acyclic graph models

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 66, Issue 1, 2004, Pages 47-61

  Roverato, Alberto ^a   Consonni, Guido ^b,c  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

^c Dipartimento di Economia Politica e Metodi Quantitativi   (Italy)

Author keywords

Bayes factor; Directed acyclic graph; Fisher information matrix; Graphical model; Group reference prior; Invariance; Jeffreys conditioning; Reference conditioning; Reparameterization

Indexed keywords

EID: 1042267795     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2004.00431.x     Document Type: Article

References (30)

1. Andersson, S. A., Madigan, D. and Perlman, M. D. (1997) On the Markov equivalence of chain graphs, undirected graphs and acyclic digraphs. Scand. J. Statist., 24, 81-102.
2. Berger, J. O. and Bernardo, J. M. (1992) On the development of the reference prior method. In Bayesian Statistics 4 (eds J. M. Bernardo, J. O. Berger, D. V. Lindley and A. F. M. Smith), pp. 35-60. Oxford: Oxford University Press.
3. Bernardo, J. M. (1979) Reference posterior distributions for Bayesian inference (with discussion). J. R. Statist. Soc. B, 41, 113-147.
4. Bernardo, J. M. and Smith, A. F. M. (1994) Bayesian Theory. Chichester: Wiley.
5. Consonni, G. and Veronese, P. (2003) Enriched conjugate and reference priors for the Wishart family on symmetric cones. Ann. Statist., 31, in the press.
6. Cowell, R. G., Dawid, A. P., Lauritzen, S. L. and Spiegelhalter, D. J. (1999) Probabilistic Networks and Expert Systems. New York: Springer.
7. Cox, D. R. and Wermuth, N. (1996) Multivariate Dependencies - Models, Analysis and Interpretation. London: Chapman and Hall.
8. Datta, G. S. and Ghosh, M. (1995) Some remarks on non-informative priors. J. Am. Statist. Ass., 90, 1357-1363.
9. Datta, G. S. and Ghosh, M. (1996) On the invariance of noninformative priors. Ann. Statist., 24, 141-159.
10. Dawid, A. P. (1981) Some matrix-variate distribution theory: notational considerations and a Bayesian application. Biometrika, 68, 265-274.
11. Dawid, A. P. and Lauritzen, S. L. (2001) Compatible prior distributions. In Bayesian Methods with Applications to Science, Policy and Official Statistics: Proc. 6th Wrld Meet. International Society for Bayesian Analysis (ed. E. I. George), pp. 109-118. Luxembourg: Office for Official Publications of the European Communities. (Available from http://www.stat.cmu.edu/ISBA/index.html.)
12. Frydenberg, M. (1990) The chain graph Markov property. Scand. J. Statist., 17, 333-353.
13. Geiger, D. and Heckerman, D. (2002) Parameters priors for directed acyclic graphical models and the characterization of several probability distributions. Ann. Statist., 30, 1412-1440.
14. Gutiérrez-Peña, E. and Rueda, R. (2003) Reference priors for exponential families. J. Statist. Planng Inf., 110, 35-54.
15. Gutiérrez-Peña, E. and Smith, A. F. M. (1995) Conjugate parameterizations for natural exponential families. J. Am. Statist. Ass., 90, 1347-1356.
16. Heckerman, D., Geiger, D. and Chickering, D. (1995) Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn., 20, 197-243.
17. Kass, R. E. and Raftery, A. E. (1995) Bayes factors. J. Am. Statist. Ass., 90, 773-795.
18. Lauritzen, S. L. (1996) Graphical Models. Oxford: Oxford University Press.
19. Lauritzen, S. L. (2001) Causal inference from graphical models. In Complex Stochastic Systems (eds O. E. Barndorff-Nielsen, D. R. Cox and C. Klüppelberg), pp. 163-107. Boca Raton: Chapman and Hall-CRC.
20. Lauritzen, S. L. and Richardson, T. S. (2002) Chain graph models and their causal interpretations (with discussion). J. R. Statist. Soc. B, 64, 321-361.
21. Leucari, V. and Consonni, G. (2003) Compatible priors for causal Bayesian networks. In Bayesian Statistics 7 (eds J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West), pp. 597-606. Oxford: Oxford University Press.
22. Lütkepohl, H. (1996) Handbook of Matrices. Chichester: Wiley.
23. Pearl, J. (2000) Causality: Models, Reasoning and Inference. Cambridge: Cambridge University Press.
24. Roverato, A. (2000) Cholesky decomposition of a hyper inverse Wishart matrix. Biometrika, 87, 99-112.
25. Roverato, A. (2002) Hyper inverse Wishart distribution for non-decomposable graphs and its application to Bayesian inference for Gaussian graphical models. Scand. J. Statist., 29, 391-411.
26. Spiegelhalter, D. and Lauritzen, S. L. (1990) Sequential updating of conditional probabilities on directed graphical structures. Networks, 20, 579-605.
27. Spirtes, P., Glymour, C. and Schemes, R. (1993) Causation, Prediction and Search. New York: Springer.
28. Verma, T. and Pearl, J. (1990) Equivalence and synthesis of causal models. In Proc. 6th Conf. Uncertainty in Artificial Intelligence (eds P. Bonissone, M. Henrion, L. N. Kanal and J. F. Lemmer), pp. 255-270. Amsterdam: North-Holland.
29. Wermuth, N. (1980) Linear recursive equations, covariance selection and path analysis. J. Am. Statist. Ass., 75, 963-972.
30. Whittaker, J. (1990) Graphical Models in Applied Multivariate Statistics. Chichester: Wiley.