ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2104.11643
46
12
v1v2 (latest)

Bayesian predictive inference without a prior

22 April 2021
P. Berti
E. Dreassi
Fabrizio Leisen
P. Rigo
L. Pratelli
ArXiv (abs)PDFHTML
Abstract

Let (Xn:n≥1)(X_n:n\ge 1)(Xn​:n≥1) be a sequence of random observations. Let σn(⋅)=P(Xn+1∈⋅∣X1,…,Xn)\sigma_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)σn​(⋅)=P(Xn+1​∈⋅∣X1​,…,Xn​) be the nnn-th predictive distribution and σ0(⋅)=P(X1∈⋅)\sigma_0(\cdot)=P(X_1\in\cdot)σ0​(⋅)=P(X1​∈⋅) the marginal distribution of X1X_1X1​. In a Bayesian framework, to make predictions on (Xn)(X_n)(Xn​), one only needs the collection σ=(σn:n≥0)\sigma=(\sigma_n:n\ge 0)σ=(σn​:n≥0). Because of the Ionescu-Tulcea theorem, σ\sigmaσ 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\sigmaσ is subjected to two requirements: (i) The resulting sequence (Xn)(X_n)(Xn​) is conditionally identically distributed, in the sense of Berti, Pratelli and Rigo (2004); (ii) Each σn+1\sigma_{n+1}σn+1​ is a simple recursive update of σn\sigma_nσn​. Various new σ\sigmaσ satisfying (i)-(ii) are introduced and investigated. For such σ\sigmaσ, the asymptotics of σn\sigma_nσn​, as n→∞n\rightarrow\inftyn→∞, is determined. In some cases, the probability distribution of (Xn)(X_n)(Xn​) is also evaluated.

View on arXiv
Comments on this paper