Bayesian predictive inference without a prior

Let be a sequence of random observations. Let be the -th predictive distribution and the marginal distribution of . In a Bayesian framework, to make predictions on , one only needs the collection . Because of the Ionescu-Tulcea theorem, can be assigned directly, without passing through the usual prior/posterior scheme. One main advantage is that no prior probability has to be selected. In this paper, is subjected to two requirements: (i) The resulting sequence is conditionally identically distributed, in the sense of Berti, Pratelli and Rigo (2004); (ii) Each is a simple recursive update of . Various new satisfying (i)-(ii) are introduced and investigated. For such , the asymptotics of , as , is determined. In some cases, the probability distribution of is also evaluated.
View on arXiv