Objective Bayes Factors for Gaussian Directed Acyclic Graphical Models

Scandinavian Journal of Statistics

Volumn 39, Issue 4, 2012, Pages 743-756

  Consonni, Guido ^a   Rocca, Luca La ^b  

^a UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

^b UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

Author keywords

Bayes factor; Bayesian model selection; Directed acyclic graph; Exponential family; Fractional Bayes factor; Gaussian graphical model; Objective Bayes; Standard conjugate prior; Structural learning

Indexed keywords

EID: 84870061071     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2011.00785.x     Document Type: Article

References (25)

1. Andersson, S. A., Madigan, D. & 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. & Pericchi, L. R. (1996). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91, 109-122.
3. Berger, J. O. & Pericchi, L. R. (2001). Objective Bayesian methods for model selection: introduction and comparison. In Model selection (ed P. Lahiri), vol. 38 of IMS Lecture Notes Monograph Series, 135-207. Institute of Mathematical Statistics, Beachwood, OH.
4. Carvalho, C. & Scott, J. (2009). Objective Bayesian model selection in Gaussian graphical models. Biometrika 96, 497-512.
5. Consonni, G. & La Rocca, L. (2011). Moment priors for Bayesian model choice with applications to directed acyclic graphs (with discussion). In Bayesian statistics 9-Proceedings of the ninth Valencia international meeting (eds J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith & M. West), 119-144. Oxford University Press, Oxford.
6. Consonni, G. & Veronese, P. (1992). Conjugate priors for exponential families having quadratic variance functions. J. Amer. Statist. Assoc. 87, 1123-1127.
7. Cowell, R. G., Dawid, P. A., Lauritzen, S. L. & Spiegelhalter, D. J. (1999). Probabilistic networks and expert systems. Springer, New York.
8. Dawid, A. P. (2003). Causal inference using influence diagrams: the problem of partial compliance. In Highly structured stochastic systems (eds P. Green, N. L. Hjort & S. Richardson), 45-81. Oxford University Press, Oxford.
9. Dawid, A. P. & Lauritzen, S. L. (1993). Hyper Markov laws in the statistical analysis of decomposable graphical models. Ann. Statist. 21, 1272-1317.
10. DeGroot, M. H. (1970). Optimal statistical decisions. McGraw-Hill, New York.
11. Diaconis, P. & Ylvisaker, D. (1979). Conjugate priors for exponential families. Ann. Statist. 7, 269-281.
12. Friedman, N. & Koller, D. (2003). Being Bayesian about network structure-A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50, 95-125.
13. Geiger, D. & Heckerman, D. (2002). Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Ann. Statist. 30, 1412-1440.
14. Gutiérrez-Peña, E. & Smith, A. F. M. (1995). Conjugate parameterizations for natural exponential families. J. Amer. Statist. Assoc. 90, 1347-1356. Erratum ibidem 91 (1996), page 1757.
15. Johnson, V. & Rossell, D. (2010). On the use of non-local prior densities in Bayesian hypothesis tests.. J. Roy. Statist. Soc. Ser. B Statist. Methodol. 72, 143-170.
16. Lauritzen, S. L. (1996). Graphical models. Oxford University Press, Oxford.
17. Lauritzen, S. L. (2001). Causal inference from graphical models. In Complex stochastic systems (eds O. E. Barndorff-Nielsen, D. R. Cox & C. Klüppelberg), vol. 87 of Monographs on Statistics and Applied Probability, 63-107. Chapman & Hall/CRC, Boca Raton, FL.
18. Letac, G. & Massam, H. (2007). Wishart distributions for decomposable graphs. Ann. Statist. 35, 1278-1323.
19. 1-statistical procedures and related topics (ed Y. Dodge), vol. 31 of IMS Lecture Notes Monograph Series, 257-270. Institute of Mathematical Statistics, Hayward, CA.
20. O'Hagan, A. (1995). Fractional Bayes factors for model comparison. J. Roy. Statist. Soc. Ser. B Statist. Methodol. 57, 99-138.
21. Perez, J. M. & Berger, J. O. (2002). Expected-posterior prior distributions for model selection. Biometrika 89, 491-511.
22. Pericchi, L. R. (2005). Model selection and hypothesis testing based on objective probabilities and Bayes factors. In Bayesian thinking: modeling and computation (eds D. Dey & C. R. Rao), vol. 25 of Handbook of Statistics, 115-149. Elsevier/North-Holland, Amsterdam.
23. Press, S. J. (1982). Applied multivariate analysis: using Bayesian and frequentist methods of inference. Krieger Publishing Company, Malabar, FL.
24. Scott, J. & Carvalho, C. (2009). Feature-inclusion stochastic search for Gaussian graphical models. J. Comput. Graph. Statist. 17, 790-808.
25. Whittaker, J. (1990). Graphical models in applied multivariate statistics. Wiley, New York.