Existence of bayesian estimates for the polychotomous quantal response models

Annals of the Institute of Statistical Mathematics

Volumn 51, Issue 4, 1999, Pages 637-656

  Chen, Ming Hui ^a   Shao, Qi Man ^b  

^a Worcester Polytechnic Institute   (United States)

^b UNIVERSITY OF OREGON   (United States)

Author keywords

Improper prior; Log log model; Logit model; Posterior distribution; Probit model

Indexed keywords

EID: 0345826170     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004027028943     Document Type: Article

References (21)

1. Agresti, A. (1990). Categorical Data Analysis, Wiley, New York.
2. Box, G. E. P. and Tiao, G. C. (1992). Bayesian Inference in Statistical Analysis, Wiley, New York.
3. Chen, M.-H. (1994). Importance weighted marginal Bayesian posterior density estimation, J. Amer. Statist. Assoc., 89, 818-824.
4. Chen, M.-H. and Dey, D. K. (1998). Bayesian modeling of correlated binary responses via scale mixture of multivariate normal link functions, Sankhyā, Ser. A, 60, 322-343.
5. Chen, M.-H. and Shao, Q.-M. (1999a). Propriety of posterior distribution for dichotomous quantal response models with general link functions, Proceedings of the American Mathematical Society (to appear).
6. Chen, M.-H. and Shao, Q.-M. (1999b). Monte Carlo estimation of Bayesian credible and HPD intervals, J. Comput. Graph. Statist., 8, 69-92.
7. CPLEX Optimization (1992). CPLEX, CPLEX Optimization Inc, Incline Village, Nevada.
8. Gelfand, A. E. and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities, J. Amer. Statist. Assoc., 85, 398-409.
9. Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
10. Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337-348.
11. Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.
12. Ibrahim, J. G. and Laud, P. W. (1991). On Bayesian analysis of generalized linear models using Jeffreys's prior, J. Amer. Statist. Assoc., 86, 981-986.
13. Jaynes, E. T. (1982). On the rationale of maximum-entropy methods, Proceedings of IEEE, 70, 939-952.
14. McCullagh, P. and Neider, J. A. FRS (1989). Generalized Linear Models, 2nd ed., Chapman & Hall, London.
15. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H. and Teller, E. (1953). Equations of state calculations by fast computing machines, Journal of Chemical Physics, 21, 1087-1092.
16. Rossi, P. (1996). Existence of Bayes estimators for the binomial logit model, Bayesian Analysis in Statistics and Econometrics - Essays in Honor of Arnold Zellner (eds. D. A. Berry, K. M. Chaloner and J. K. Geweke), 91-100, Wiley, New York.
17. Stokes, M. E., Davis, C. S. and Koch, G. G. (1995). Categorical Data Analysis Using the SAS System, SAS Institute Inc., Cary, North Carolina.
18. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion), Ann. Statist., 22, 1701-1762.
19. Wedderburn, R. W. M. (1976). On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models, Biometrika, 63, 27-32.
20. Zellner, A. (1997). Past and recent results on maximal data information priors, Bayesian Analysis in Econometrics and Statistics: The Zellner View and Papers, 127-148, Edward Elgar, Cheltenham.
21. Zellner, A. and Rossi, P. E. (1984). Bayesian analysis of dichotomous quantal response models, J. Econometrics, 25, 365-393.