A class of models for Bayesian predictive inference (original) (raw)

In a Bayesian framework, to make predictions on a sequence X1, X2,. .. of random observations, the inferrer needs to assign the predictive distributions σn(•) = P Xn+1 ∈ • | X1,. .. , Xn. In this paper, we propose to assign σn directly, without passing through the usual prior/posterior scheme. One main advantage is that no prior probability has to be assessed. The data sequence (Xn) is assumed to be conditionally identically distributed (c.i.d.) in the sense of [4]. To realize this programme, a class Σ of predictive distributions is introduced and investigated. Such a Σ is rich enough to model various real situations and (Xn) is actually c.i.d. if σn belongs to Σ. Furthermore, when a new observation Xn+1 becomes available, σn+1 can be obtained by a simple recursive update of σn. If µ is the a.s. weak limit of σn, conditions for µ to be a.s. discrete are provided as well.