An analytic example of latent information prior

TL;DR

This paper analytically derives the latent information prior for one-step ahead binomial prediction, confirming Komaki's numerical results and identifying the minimax predictive distribution.

Contribution

It provides an explicit analytical form of the latent information prior in a binomial setting, enhancing understanding of objective priors.

Findings

Latent information prior is discrete in this case.

Analytical derivation confirms previous numerical results.

Identifies the minimal complete class and minimax predictive distribution.

Abstract

Recently Komaki proposed latent information priors as an objective prior. In this short article, we consider the one-step ahead prediction based on one-sample under the binomial model. In this specific case, the latent information prior is derived analytically and shown to be a discrete prior. It verifies the numerical result by Komaki. As a by-product, we obtain the minimal complete class, the minimax predictive distribution.