The mode oriented stochastic search (MOSS) algorithm for log-linear models with conjugate priors

Statistical Methodology

Volumn 7, Issue 3, 2010, Pages 240-253

  Dobra, Adrian ^a   Massam, Héléne ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b YORK UNIVERSITY   (Canada)

Author keywords

Bayesian analysis; Contingency table; Hierarchical log linear model; Markov chain Monte Carlo; Model selection; Stochastic search

Indexed keywords

EID: 77950918021     PISSN: 15723127     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.stamet.2009.04.002     Document Type: Article

References (33)

1. Bishop Y.M.M., Fienberg S.E., and Holland P.W. Discrete Multivariate Analysis: Theory and Practice (1975), M.I.T. Press, Cambridge, MA
2. Edwards D.E., and Havranek T. A fast procedure for model search in multidimensional contingency tables. Biometrika 72 (1985) 339-351
3. Agresti A. Categorical Data Analysis (1990), Wiley
4. Whittaker J. Graphical Models in Applied Multivariate Statistics (1990), John Wiley & Sons
5. Fienberg S.E., and Rinaldo A. Three centuries of categorical data analysis: Log-linear models and maximum likelihood estimation. J. Statist. Plann. Inference 137 (2007) 3430-3445
6. Clyde M., and George E.I. Model uncertainty. Statist. Sci. 19 (2004) 81-94
7. Dellaportas P., and Forster J.J. Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models. Biometrika 86 (1999) 615-633
8. Madigan D., and Raftery A. Model selection and accounting for model uncertainty in graphical models using Occam's window. J. Amer. Statist. Assoc. 89 (1994) 1535-1546
9. Madigan D., and York J. Bayesian graphical models for discrete data. International Statistical Review 63 (1995) 215-232
10. Madigan D., and York J. Bayesian methods for estimation of the size of a closed population. Biometrika 84 (1997) 19-31
11. Tarantola C. MCMC model determination for discrete graphical models. Stat. Modelling 4 (2004) 39-61
12. Dellaportas P., and Tarantola C. Model determination for categorical data with factor level merging. J. R. Stat. Soc. Ser. B 67 (2005) 269-283
13. Jones B., Carvalho C., Dobra A., Hans C., Carter C., and West M. Experiments in stochastic computation for high-dimensional graphical models. Statist. Sci. 20 (2005) 388-400
14. Hans C., Dobra A., and West M. Shotgun stochastic search for "large p" regression. J. Amer. Statist. Assoc. 102 (2007) 507-516
15. Massam H., Liu J., and Dobra A. A conjugate prior for discrete hierarchical log-linear models. Ann. Statist. (2009)
16. Piccioni M. Independence structure of natural conjugate densities to exponential families and the Gibbs sampler. Scand. J. Statist. 27 (2000) 111-127
17. Dawid A.P., and Lauritzen S.L. Hyper Markov laws in the statistical analysis of decomposable graphical models. Ann. Statist. 21 (1993) 1272-1317
18. Knuiman M., and Speed T. Incorporating prior information into the analysis of contingency tables. Biometrics 44 (1988) 1061-1071
19. King R., and Brooks S.P. Prior induction for log-linear models for general contingency table analysis. Ann. Statist. 29 (2001) 715-747
20. Diaconis P., and Ylvisaker D. Conjugate priors for exponential families. Ann. Statist. 7 (1979) 269-281
21. Lauritzen S.L. Graphical Models (1996), Clarendon Press, Oxford
22. Darroch J., and Speed T. Additive and multiplicative models and interaction. Ann. Statist. 11 (1983) 724-738
23. Tierney L., and Kadane J. Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81 (1986) 82-86
24. Dobra A., and Fienberg S.E. Bounds for cell entries in contingency tables given marginal totals and decomposable graphs. Proc. Natl. Acad. Sci. 97 (2000) 11185-11192
25. Godsill S.J. On the relationship between Markov chain Monte Carlo methods for model uncertainty. J. Comput. Graph. Statist. 10 (2001) 1-19
26. Green P.J. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 (1995) 711-732
27. Carlin B.P., and Chib S. Bayesian model choice via Markov chain Monte Carlo. J. R. Stat. Soc. Ser. B 57 (1995) 473-484
28. Raftery A.E., Madigan D., and Hoeting J.A. Bayesian model averaging for linear regression models. J. Amer. Statist. Assoc. 92 (1997) 179-191
29. Kass R.E., and Raftery A.E. Bayes factors. J. Amer. Statist. Assoc. 90 (1995) 773-795
30. Robert C.P. Discretization and MCMC Convergence Assessment. Lecture Notes in Statistics vol. 135 (1998), Springer-Verlag
31. Gelman A., Carlin J.B., Stern H.S., and Rubin D. Bayesian Data Analysis. second ed. Texts in Statistical Science Series (2004), Chapman & Hall
32. Schafer J.L. Analysis of Incomplete Multivariate Data (1997), Chapman & Hall, London
33. Asci C., and Piccioni M. Functionally compatible local characteristics for the local specification of priors in graphical models. Scand. J. Statist. 34 (2007) 829-840