Bayesian Predictive Inference Without a Prior

Berti, Patrizia; Dreassi, Emanuela; Leisen, Fabrizio; Pratelli, Luca; Rigo, Pietro

Abstract

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. To make predictions on (Xn), a Bayesian forecaster 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. This point of view is adopted in this paper. The choice of σ is only subjected to two requirements: (i) The resulting sequence (Xn) is conditionally identically distributed, in the sense of [4]; (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.

Citation

Berti, P., Dreassi, E., Leisen, F., Pratelli, L., & Rigo, P. (2023). Bayesian Predictive Inference Without a Prior. Statistica Sinica, 33(4), 2405-2429. https://doi.org/10.5705/ss.202021.0238

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2022
• Online Publication Date: Aug 2, 2023
• Publication Date: 2023-10
• Deposit Date: Mar 21, 2022
• Publicly Available Date: Mar 25, 2022
• Journal: Statistica Sinica
• Print ISSN: 1017-0405
• Electronic ISSN: 1996-8507
• Publisher: Academia Sinica, Institute of Statistical Science
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 4
• Pages: 2405-2429
• DOI: https://doi.org/10.5705/ss.202021.0238
• Keywords: Statistics, Probability and Uncertainty; Statistics and Probability
• Public URL: https://nottingham-repository.worktribe.com/output/7642470
• Publisher URL: https://www3.stat.sinica.edu.tw/statistica/J33N4/J33N406/J33N406.html