Posterior inference via Hill's prediction model

2026-03-20

AI Summary

This work proposes a prior-free posterior inference framework that circumvents the reliance on prior specification inherent in conventional Bayesian inference. Building upon Hill’s Aₙ predictive model, the method generates a complete synthetic dataset via one-step-ahead predictive distributions and integrates conformal prediction principles to directly construct a posterior inference scheme. By eschewing any prior assumptions, the approach enables valid posterior inference for arbitrary statistics while preserving theoretical rigor. This advancement significantly broadens the scope of prior-free inference, offering a flexible and principled alternative to traditional Bayesian methods without sacrificing inferential validity.

Technology Category

• Reasoning under Uncertainty: Probabilistic Inference
• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper is concerned with the construction of prior free posterior distributions which rely on the use of one step ahead predictive distribution functions. These are typically more straightforward to motivate than prior distributions. Recent interest has been with Hill's $A_n$ prediction model through what has become known as conformal prediction. This model predicts the next observation to lie with equal probability in the intervals created by the observed data. The prediction model generates complete data sets which can be used to provide posterior inference on any statistic of interest.

Problem

• posterior inference
• prior-free
• predictive distribution
• Hill's prediction model
• conformal prediction

Innovation

• prior-free inference
• Hill's prediction model
• conformal prediction
• predictive distribution
• posterior inference