On some effects of the choice of finitely additive priors when the basis model belongs to the truncated exponential family. (Italian. English summary) Zbl 0692.62029

Carota, Cinzia; Corielli, Francesco

Riv. Mat. Sci. Econ. Soc. 11, No. 1-2, 147-161 (1988).

Summary: We use finitely additive prior distributions with the aim of maximizing the association between the elements of an exchangeable process and we discuss the effects and the meaning of these assumptions (§ 1 and § 2). Applying these distributions to the canonical parameter of elements of the truncated exponential family of distributions we obtain (§ 3) the expression for the joint distribution of a vector of observations (theorem 1). In § 4 a different method of proof is suggested for some results pertaining to theorem 1. In § 5, under mild hypotheses, we obtain some results about the expectation of the predictive distribution. We examine some consequences of our assumptions on the predictive and posterior distributions.

MSC:

62F15	Bayesian inference
62E15	Exact distribution theory in statistics

Keywords:

finitely additive prior distributions; exchangeable process; truncated exponential family of distributions; joint distribution; expectation of the predictive distribution