# Quasi-Bayes empirical Bayes: a sequential approach to the Poisson compound decision problem

arXiv: https://arxiv.org/abs/2411.07651 · HTML: https://mlsanity.com/paper/2411.07651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [Two Modeling Strategies for Empirical Bayes Estimation](https://mlsanity.com/paper/1409.2677/) (2014)
- [Sharp regret bounds for empirical Bayes and compound decision problems](https://mlsanity.com/paper/2109.03943/) (2021)
- [Quasi-Bayes properties of a recursive procedure for mixtures](https://mlsanity.com/paper/1902.10708/) (2019)
- [Optimal empirical Bayes estimation for the Poisson model via minimum-distance methods](https://mlsanity.com/paper/2209.01328/) (2022)
- [A General Framework for Empirical Bayes Estimation in Discrete Linear Exponential Family](https://mlsanity.com/paper/1910.08997/) (2019)

## Abstract (arXiv)

The Poisson compound decision problem is a long-standing problem is statistics, for which empirical Bayes methods are commonly used to estimate Poisson means in static or batch settings. We consider this problem in a streaming, or online, framework. Building on a quasi-Bayesian approach based on Newton's algorithm, we develop a sequential estimate that is easy to evaluate, computationally efficient, and has constant per-observation cost as the data accrue. We establish frequentist guarantees for the proposed estimate, including consistency and asymptotic optimality, with optimality understood as vanishing excess Bayes risk, or regret. Empirical performance is assessed through simulation studies and comparisons with benchmark procedures.