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

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Data Science & Analytics · Depth: Expert, extended

Summary

The paper introduces a quasi-Bayes empirical Bayes methodology for the Poisson compound decision problem, specifically designed for streaming or online data environments. This sequential approach, which relies on Newton's algorithm, yields Poisson mean estimates that are easy to evaluate, computationally efficient, and maintain a constant computational cost as data volume increases. The methodology's large sample asymptotic properties are investigated, providing frequentist guarantees through regret analysis. Empirical validation on synthetic data and real-world datasets, including 166,783 Twitter tweets and 9461 auto accident claims, demonstrates that the proposed method outperforms nonparametric empirical Bayes and competes effectively with nonparametric maximum likelihood, minimum squared Hellinger distance, and parametric Bayes empirical Bayes.

Key takeaway

For research scientists developing online statistical models, this quasi-Bayes empirical Bayes method offers a robust solution for streaming Poisson data. Its constant computational cost and strong asymptotic guarantees make it ideal for high-velocity count data, enabling timely, accurate parameter estimation without recomputing the entire dataset. You should consider implementing Newton's algorithm for real-time applications requiring efficient mean estimation.

Key insights

Newton's algorithm enables efficient, sequential Poisson mean estimation for streaming data with strong guarantees.

Principles

• Sequential updates maintain computational efficiency.
• Quasi-Bayes offers lower computational cost.
• Regret analysis provides frequentist guarantees.

Method

Recursively update the prior distribution G using Newton's algorithm with a learning rate αn=(α+n)−γ, then apply the plug-in estimate θ^Gn(y).

In practice

• Monitor social media analytics.
• Analyze network traffic in real-time.
• Estimate insurance claim rates.

Topics

• Empirical Bayes
• Poisson Compound Decision
• Streaming Data
• Newton's Algorithm
• Sequential Estimation
• Count Data Analytics

Best for: AI Scientist, Research Scientist

Related on AIssential

• Bayesian Inference of Contextual Bandit Policies via Empirical Likelihood — Empirical likelihood enables robust Bayesian inference for contextual bandit policies, even with small datasets.
• Non-asymptotic quantisation of spherically symmetric distributions — This paper addresses the challenge of optimal quantisation in high dimensions ($d$), where Zador's theorem requires an astronomically large sample size ($n$) for its asymptotic behavior to be observed.
• Naïve Bayes: The Algorithm That’s Wrong About Everything But Right About Results — Naïve Bayes effectively classifies by combining prior class probabilities with feature likelihoods, despite a "naïve" independence assumption.
• Extending Causal Metamodeling to a non-Markovian Queue — MDBNs can now perform causal metamodeling for non-Markovian systems by approximating non-exponential distributions with phase-type distributions.
• Asymptotically Log-Optimal Bayes-Assisted Confidence Sequences for Bounded Means — Bayes-assisted confidence sequences leverage prior information for efficiency without sacrificing anytime-valid coverage.
• Scalable Model-Based Clustering with Sequential Monte Carlo — A novel SMC algorithm improves scalability for online clustering by decomposing problems into independent subproblems.

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.