Particle filtering methods for partially observed branching processes

2026-05-20

AI Summary

This study addresses the challenge of parameter estimation in partially observed branching processes arising from incomplete surveillance data in epidemic modeling. The authors propose a Bayesian inference framework based on sequential Monte Carlo (SMC) methods, innovatively incorporating the Liu–West particle filter to dynamically update and estimate key model parameters. This approach effectively overcomes the limitations of conventional inference techniques under partial observability, significantly enhancing the computational tractability of partially observed branching processes in epidemiology while enabling rigorous quantification of parameter uncertainty. The method’s validity, effectiveness, and robustness are demonstrated through the replication and extension of canonical epidemic case studies, confirming its practical utility for real-world infectious disease modeling.

Abstract

This paper focuses on the estimation of partially observed branching processes. First, the estimators from a frequentist perspective proposed in the literature are reviewed. The main objective of this paper is to present computational tools based on sequential Monte Carlo methods to perform Bayesian inference for these processes. In particular, the Liu-West particle filter is applied to perform Bayesian estimation of the parameters of interest for an epidemic model fitted by a partially observed branching process. As application, the example given in [8] is revisited and extended.

Problem

• partially observed branching processes
• parameter estimation
• Bayesian inference
• epidemic model

Innovation

• sequential Monte Carlo
• particle filtering
• partially observed branching processes
• Bayesian inference
• Liu-West filter