Bayesian Estimation of Multinomial Cell Probabilities Incorporating Information from Aggregated Observations

TL;DR

This paper develops Bayesian estimators for multinomial probabilities using Jeffreys prior, demonstrating how incorporating aggregated data improves estimation accuracy under entropy loss.

Contribution

It introduces a method to incorporate side information from aggregated data into Bayesian estimation of multinomial probabilities, enhancing estimator performance.

Findings

Inclusion of side information improves estimation accuracy.

Jeffreys prior-based Bayes estimators outperform traditional methods.

The approach is effective under entropy loss.

Abstract

In this note, we consider the problem of estimating multinomial cell probabilities under the entropy loss when side information in aggregated data is available. We use the Jeffreys prior to obtain Bayes estimators. It is shown that by incorporating the side information, we can construct an improved estimator.