Conjugate Priors for Exponential Families Having Quadratic Variance Functions
β Scribed by Guido Consonni and Piero Veronese
- Book ID
- 125249769
- Publisher
- American Statistical Association
- Year
- 1992
- Tongue
- English
- Weight
- 844 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0162-1459
- DOI
- 10.2307/2290650
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π SIMILAR VOLUMES
Within the framework of the quadratic natural exponential families we construct a basis of polynomials orthogonal with respect to the posterior density. This construction is adapted from Walter and Hamedani (Ann. Statist. 3 (1991) 1191) and we exploit them to establish lower bounds for the posterior
A generalization to N" of a property of natural exponential families on ~ with simple quadratic variances is obtained. This property yields the original density in terms of the Laplace transform of the conjugate prior for the natural parameter.