Bayesian models for sparse probability tables

Annals of Statistics

Volumn 24, Issue 5, 1996, Pages 2178-2198

  Smith, Jim Q ^a   Queen, Catriona M ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Bayesian probability estimation; Constraint graph; Contingency tables; Decomposable graph; Generalized Dirichlet distributions; Separation of likelihood

Indexed keywords

EID: 0030363429     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362316     Document Type: Article

References (22)

1. CARLSON, B. C. (1977). Special Functions of Applied Mathematics. Academic Press, New York.
2. DAWID, A. P. and DICKEY, J. M. (1977). Likelihood and Bayesian inference from selectively reported data. J. Amer. Statist. Assoc. 72 845-850.
3. DAWID, A. P. and LAURITZEN, S. L. (1993). Hyper Markov laws in the statistical analysis of decomposable graphical models. Ann. Statist. 21 1272-1317.
4. DECHTER, R., DECHTER, A. and PEARL, J. (1990). Optimisation in constraint networks. In Influence Diagrams, Belief Nets and Decision Analysis (R. M. Oliver and J. Q. Smith, eds.) 411-425. Wiley, New York.
5. DECHTER, R. and PEARL, J. (1987). Network-based heuristics for constraint satisfaction problems. Artificial Intelligence 34 1-38.
6. DICKEY, J. M. (1983). Multiple hypergeometric functions: probabilistic interpretations of statistical uses. J. Amer. Statist. Assoc. 78 628-637.
7. DICKEY, J. M., JIANG, J. and KADANE J. B. (1987). Bayesian methods for censored categorical data. J. Amer. Statist. Assoc. 82 773-781.
8. GENG, Z. and ASANO, C. (1989). Bayesian estimation methods for catagorical data with misclassification. Comm. Statist. Theory Methods 18 2935-2954.
9. GILKS, W. R. (1992). Bayes derivative-free adaptive rejection sampling for Gibbs sampling. In Bayesian Statistics (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 641-649. Oxford Science Publications.
10. GRANDY, W. T., JR. (1985). Incomplete information in generalised inverse problems. In Maximum Entropy and Bayesian Methods in Inverse Problems (C. R. Smith and W. T. Grandy, Jr., eds.) 41-72. Reidel, Boston.
11. GROVER, R. and SRINIVASAN V. (1987). A simultaneous approach to market segmentation and market structuring. Journal of Marketing Research 3 139-153.
12. JOHNSON, N. L. and KOTZ, S. (1972). Distributions in Statistics, Continuous Multivariate Distributions. Wiley, New York.
13. LAURITZEN, S. L., SPEED, T. P. and VUAGAN, K. (1984). Decomposable graphs and hypergraphs. J. Austral. Math. Soc. Ser. A 36 12-29.
14. LAURITZEN, S. and SPIEGELHALTER, D. J. (1988). Local computations with probabilities on graphical structures and their applications to expert systems (with discussion). J. Roy. Statist. Soc. Ser. B 50 157-224.
15. QUEEN, C. M. (1991). Bayesian graphical forecasting models for business time series. Ph.D. dissertation, Univ. Warwick.
16. QUEEN, C. M. (1994). Using the multi-regression dynamic model to forecast brand sales in a competitive product market. The Statistician 43 87-98.
17. QUEEN, C. M., SMITH, J. Q. and JAMES, D. M. (1994). Bayesian forecasts in markets with overlapping structures. International Journal of Forecasting 10 209-233.
18. RUBIN, D. B. (1976). Inference and missing data. Biometrika 63 581-592.
19. SMITH, J. Q. and QUEEN, C. M. (1992). Bayesian models of partially segmented markets. Research Report 232, Univ. Warwick.
20. TANNER, M. A. and WONG, W. H. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82 528-550.
21. TARJAN, R. E. and YANNAKAKIS, M. (1984). Simple linear time algorithms to test chordality of graphs, test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13 566-579.
22. VARDI, Y. and LEE, D. (1993). From image deblurring to optimal investments: maximum likelihood solutions for positive linear inverse problems (with discussion). J. Roy. Statist. Soc. Ser. B 55 569-612.