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Propriety of posterior distribution for dichotomous quantal response models
Author(s):
Ming-Hui
Chen;
Qi-Man
Shao
Journal:
Proc. Amer. Math. Soc.
129
(2001),
293-302.
MSC (2000):
Primary 62F15, 62E15, 62J12
Posted:
August 17, 2000
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Abstract:
In this article, we investigate the property of posterior distribution for dichotomous quantal response models using a uniform prior distribution on the regression parameters. Sufficient and necessary conditions for the propriety of the posterior distribution with a general link function are established. In addition, the sufficient conditions for the existence of the posterior moments and the posterior moment generating function are also obtained. Finally, the relationship between the propriety of posterior distribution and the existence of the maximum likelihood estimate is examined.
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Additional Information:
Ming-Hui
Chen
Affiliation:
Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280
Email:
mhchen@wpi.edu
Qi-Man
Shao
Affiliation:
Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email:
shao@math.uoregon.edu
DOI:
10.1090/S0002-9939-00-05513-1
PII:
S 0002-9939(00)05513-1
Keywords:
Improper prior,
logit model,
log-log model,
probit model,
maximum likelihood estimate
Received by editor(s):
March 3, 1999
Posted:
August 17, 2000
Additional Notes:
Research of the first author was partially supported by the National Science Foundation under Grant No. DMS-9702172, and of the second author by the National Science Foundation under Grant No. DMS-9802451
Communicated by:
Wei Y. Loh
Copyright of article:
Copyright
2000,
American Mathematical Society
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