2021/04/22 by Berti, Patrizia, Dreassi, Emanuela, Leisen, Fabrizio +2 · 2 citations
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2104.11643
Let (Xn:n≥ 1) be a sequence of random observations. Let σn(⋅)=P(Xn+1∈⋅| X1,…,Xn) be the n-th predictive distribution and σ0(⋅)=P(X1∈⋅) the marginal distribution of X1. In a Bayesian framework, to make predictions on (Xn), one only needs the collection σ=(σn:n≥ 0). Because of the Ionescu-Tulcea theorem, σ 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, σ is subjected to two requirements: (i) The resulting sequence (Xn) is conditionally identically distributed, in the sense of Berti, Pratelli and Rigo (2004); (ii) Each σn+1 is a simple recursive update of σn. Various new σ satisfying (i)-(ii) are introduced and investigated. For such σ, the asymptotics of σn, as n→∞, is determined. In some cases, the probability distribution of (Xn) is also evaluated.