Justin J. Slater | Searcharxiv

arXiv2026

Sequential Importance Sampling for Thinned Count Autoregressions via Latent Gaussian Transformations

Thinned count autoregressions are popular for modelling infectious disease surveillance data due to their flexibility and interpretability. However, such a model is challenging to fit since it involves high-dimensional and serially correlated integer-valued unknowns. One solution is to consider an analogous continuous-valued surrogate model whose values are post-hoc mapped to integers. This procedure produces biased estimates as inference is performed using samples from such a surrogate model and not the thinned count autoregression itself. In this work, we propose a sequential importance sampling procedure to correct this misspecified model. We demonstrate its validity in a simulation study and its applicability for epidemic curve reconstruction using rotavirus data from Germany and meningococcus data from France.

stat.ME↗

arXiv2025

Modelling Under-Reported Data: Pitfalls of Naïve Approaches and a New Statistical Framework for Epidemic Curve Reconstruction

Count-valued autoregressions are widely used to analyse time-series of reported infectious-disease cases because of their close connection with discrete-time transmission models. However, when such models are applied directly to under-reported case counts, their mechanistic interpretation can break down. We establish new theoretical results quantifying the consequences of ignoring under-reporting in these models. To address this issue, reported cases are often modelled as a binomially thinned version of an underlying count process, but such models are difficult to fit because the unobserved true counts are serially correlated and integer-valued. We develop a new statistical framework for under-reported infectious-disease data that uses a normal-normal approximation to a broad class of thinned count autoregressions and then accurately maps this continuous process back to the integers. Through simulations and applications to rotavirus incidence in a German state and Covid-19 incidence in English conurbations, we demonstrate that our approach both retains the mechanistic appeal of thinned autoregressions and substantially simplifies inference.

stat.AP↗