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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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