arXiv subjects

Lloyd A. C. Chapman

Publications and source records attributed to Lloyd A. C. Chapman.

6 recordsLinked to original sources

arXiv2026

Scalable Bayesian inference for time-discretised Markov jump processes via exchangeable particle Gibbs

Inference in stochastic reaction-network models, such as the susceptible-exposed-infectious-recovered (SEIR) epidemic model, is crucial for understanding the dynamics of interacting systems in epidemiology, ecology, and systems biology. These models are typically represented as Markov jump processes (MJPs), with discrete, noisy observations and intractable likelihoods. Particle Markov chain Monte Carlo (PMCMC) offers a natural mechanism for inference on these hidden Markov models, but, even in moderate dimensional state spaces, particle degeneracy typically leads to poor mixing of the PMCMC algorithm. This paper focuses on improving the efficiency of particle Gibbs for inference on reaction networks by addressing the degeneracy problem. Building on recent work on the exchangeable particle Gibbs (xPG) sampler for diffusions, this paper develops a novel version of xPG tailored to discrete-state-space reaction networks, where randomness is driven by Poisson processes rather than Brownian motion. We focus on the $τ$-leap discretisation of the MJPs. The proposed method retains the exchangeability framework of xPG while adapting it to the structural and computational challenges specific to reaction networks. The new method is applied to several examples, including four coupled SEIR models, where it substantially improves mixing efficiency compared with standard particle Gibbs. In this example, xPG improves sample efficiency by more than an order of magnitude relative to standard particle Gibbs, making inference feasible in hours rather than weeks. As part of our tuning strategy, we provide a mechanism for tuning the number of particles that is applicable more generally, to any particle Gibbs algorithm.

stat.CO↗

arXiv2026

FluxDisco: Symbolic Regression for Stoichiometric Dynamical Systems via Monte Carlo Graph Search

Dynamical symbolic regression methods identify governing differential equations from noisy data, balancing interpretability and predictive accuracy. However, standard methods often produce expressions that violate known physical laws. To address this, we propose FluxDisco, a physics-informed framework tailored for flux-based, stoichiometric ODE systems. By leveraging a known stoichiometry, we reduce the expression search space and ensure physical adherence. Our framework adapts the Monte Carlo Graph Search algorithm for the unique challenges associated with joint flux discovery of stoichiometric systems. We evaluate our method across a range of physical and biological systems, demonstrating its ability to accurately recover governing dynamics through interpretable equations.

stat.ML↗

arXiv2026

Non-centred Bayesian inference for discrete-valued state-transition models: the Rippler algorithm

Stochastic state-transition models of infectious disease transmission can be used to deduce relevant drivers of transmission when fitted to data using statistically principled methods. Fitting this individual-level data requires inference on individuals' unobserved disease statuses over time, which form a high-dimensional and highly correlated state space. We introduce a novel Bayesian (data-augmentation Markov chain Monte Carlo) algorithm for jointly estimating the model parameters and unobserved disease statuses, which we call the Rippler algorithm. This is a non-centred method that can be applied to any individual-based state-transition model. We compare the Rippler algorithm to the state-of-the-art inference methods for individual-based stochastic epidemic models and find that it performs better than these methods as the number of disease states in the model increases.

stat.ME↗

arXiv2025

Non-centering for discrete-valued state transition models: an application to ESBL-producing E. coli transmission in Malawi

Infectious disease transmission is often modelled by discrete-valued stochastic state-transition processes. Due to a lack of complete data, Bayesian inference for these models often relies on data-augmentation techniques. These techniques are often inefficient or time consuming to implement. We introduce a novel data-augmentation Markov chain Monte Carlo method for discrete-time individual-based epidemic models, which we call the Rippler algorithm. This method uses the transmission model in the proposal step of the Metropolis-Hastings algorithm, rather than in the accept-reject step. We test the Rippler algorithm on simulated data and apply it to data on extended-spectrum beta-lactamase (ESBL)-producing E. coli collected in Blantyre, Malawi. We compare the Rippler algorithm to two other commonly used Bayesian inference methods for partially observed epidemic data, and find that it has a good balance between mixing speed and computational complexity.

stat.ME↗

arXiv2020

Developments in statistical inference when assessing spatiotemporal disease clustering with the tau statistic

The tau statistic $τ$ uses geolocation and, usually, symptom onset time to assess global spatiotemporal clustering from epidemiological data. We test different factors that could affect graphical hypothesis tests of clustering or bias clustering range estimates based on the statistic, by comparison with a baseline analysis of an open access measles dataset. From re-analysing this data we find that the spatial bootstrap sampling method used to construct the confidence interval for the tau estimate and confidence interval (CI) type can bias clustering range estimates. We suggest that the bias-corrected and accelerated (BCa) CI is essential for asymmetric sample bootstrap distributions of tau estimates. We also find evidence against no spatiotemporal clustering, $p$-value $\in$ [0,0.014] (global envelope test). We develop a tau-specific modification of the Loh & Stein spatial bootstrap sampling method, which gives more precise bootstrapped tau estimates and a 20% higher estimated clustering endpoint than previously published (36.0m; 95% BCa CI (14.9, 46.6), vs 30m) and an equivalent increase in the clustering area of elevated disease odds by 44%. What appears a modest radial bias in the range estimate is more than doubled on the areal scale, which public health resources are proportional to. This difference could have important consequences for control. Correct practice of hypothesis testing of no clustering and clustering range estimation of the tau statistic are illustrated in the Graphical abstract. We advocate proper implementation of this useful statistic, ultimately to reduce inaccuracies in control policy decisions made during disease clustering analysis.

stat.ME↗

arXiv2019

The spatiotemporal tau statistic: a review

Introduction The tau statistic is a recent second-order correlation function that can assess the magnitude and range of global spatiotemporal clustering from epidemiological data containing geolocations of individual cases and, usually, disease onset times. This is the first review of its use, and the aspects of its computation and presentation that could affect inferences drawn and bias estimates of the statistic. Methods Using Google Scholar we searched papers or preprints that cited the papers that first defined/reformed the statistic. We tabulated their key characteristics to understand the statistic's development since 2012. Results Only half of the 16 studies found were considered to be using true tau statistics, but their inclusion in the review still provided important insights into their analysis motivations. All papers that used graphical hypothesis testing and parameter estimation used incorrect methods. There is a lack of clarity over how to choose the time-relatedness interval to relate cases and the distance band set, that are both required to calculate the statistic. Some studies demonstrated nuanced applications of the tau statistic in settings with unusual data or time relation variables, which enriched understanding of its possibilities. A gap was noticed in the estimators available to account for variable person-time at risk. Discussion Our review comprehensively covers current uses of the tau statistic for descriptive analysis, graphical hypothesis testing, and parameter estimation of spatiotemporal clustering. We also define a new estimator of the tau statistic for disease rates. For the tau statistic there are still open questions on its implementation which we hope this review inspires others to research.

stat.AP↗