Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology

Fuente: arXiv
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Main Authors: Lewis, Angus, Parrella, Antonio, Maclean, John, Black, Andrew J.
Format: Preprint
Published: 2025
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author Lewis, Angus
Parrella, Antonio
Maclean, John
Black, Andrew J.
author_facet Lewis, Angus
Parrella, Antonio
Maclean, John
Black, Andrew J.
contents We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo, can be computationally challenging when the populations that are being modelled grow exponentially or the time series is long. Instead, we derive a Gaussian approximation for the transition function of the process that leads to a Kalman filtering algorithm that runs in a time independent of the population sizes. We also develop a hybrid approach for when populations are smaller and the approximation is less applicable. We investigate the performance of our approximation and algorithms to both a simple and a complex epidemic model, finding good adherence to the true posterior distributions in both cases with large computational speed-ups in most cases. We also apply our method to a COVID-19 dataset with time dependent parameters where exact methods are intractable due to the population sizes involved.
format Preprint
id arxiv_https___arxiv_org_abs_2511_22833
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology
Lewis, Angus
Parrella, Antonio
Maclean, John
Black, Andrew J.
Methodology
Probability
60J80, 60J28, 60J22
We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo, can be computationally challenging when the populations that are being modelled grow exponentially or the time series is long. Instead, we derive a Gaussian approximation for the transition function of the process that leads to a Kalman filtering algorithm that runs in a time independent of the population sizes. We also develop a hybrid approach for when populations are smaller and the approximation is less applicable. We investigate the performance of our approximation and algorithms to both a simple and a complex epidemic model, finding good adherence to the true posterior distributions in both cases with large computational speed-ups in most cases. We also apply our method to a COVID-19 dataset with time dependent parameters where exact methods are intractable due to the population sizes involved.
title Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology
topic Methodology
Probability
60J80, 60J28, 60J22
url https://arxiv.org/abs/2511.22833