2023 A Probabilistic View on Predictive Constructions for Bayesian Learning
Patrizia Berti, Emanuela Dreassi, Fabrizio Leisen, Luca Pratelli, Pietro Rigo
Author Affiliations +
Statist. Sci. Advance Publication 1-15 (2023). DOI: 10.1214/23-STS884


Given a sequence X=(X1,X2,) of random observations, a Bayesian forecaster aims to predict Xn+1 based on (X1,,Xn) for each n0. To this end, in principle, she only needs to select a collection σ=(σ0,σ1,), called “strategy” in what follows, where σ0(·)=P(X1·) is the marginal distribution of X1 and σn(·)=P(Xn+1·|X1,,Xn) the nth predictive distribution. 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 is to be selected. In a nutshell, this is the predictive approach to Bayesian learning. A concise review of the latter is provided in this paper. We try to put such an approach in the right framework, to make clear a few misunderstandings, and to provide a unifying view. Some recent results are discussed as well. In addition, some new strategies are introduced and the corresponding distribution of the data sequence X is determined. The strategies concern generalized Pólya urns, random change points, covariates and stationary sequences.


We are grateful to Federico Bassetti and Paola Bortot for very useful conversations.


Download Citation

Patrizia Berti. Emanuela Dreassi. Fabrizio Leisen. Luca Pratelli. Pietro Rigo. "A Probabilistic View on Predictive Constructions for Bayesian Learning." Statist. Sci. Advance Publication 1 - 15, 2023. https://doi.org/10.1214/23-STS884


Published: 2023
First available in Project Euclid: 23 February 2023

Digital Object Identifier: 10.1214/23-STS884

Keywords: Bayesian inference , conditional identity in distribution , exchangeability , predictive distribution , sequential predictions , stationarity

Rights: Copyright © 2023 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Advance Publication
Back to Top