Posterior inference via Hill's prediction model

TL;DR

This paper explores a prior-free Bayesian inference method using Hill's prediction model, which employs one-step ahead predictive distributions to generate posterior distributions without traditional priors.

Contribution

It introduces a novel approach to posterior inference based on Hill's conformal prediction model, simplifying the process by avoiding prior specification.

Findings

Provides a framework for prior-free posterior inference

Demonstrates the use of Hill's prediction model for statistical analysis

Shows the model's effectiveness in generating complete data sets

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.