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Propriety of posterior distribution for dichotomous quantal response models


Authors: Ming-Hui Chen and Qi-Man Shao
Journal: Proc. Amer. Math. Soc. 129 (2001), 293-302
MSC (2000): Primary 62F15, 62E15, 62J12
DOI: https://doi.org/10.1090/S0002-9939-00-05513-1
Published electronically: August 17, 2000
MathSciNet review: 1694452
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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: https://doi.org/10.1090/S0002-9939-00-05513-1
Keywords: Improper prior, logit model, log-log model, probit model, maximum likelihood estimate
Received by editor(s): March 3, 1999
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society

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