Sequential Importance Sampling for Thinned Count Autoregressions via Latent Gaussian Transformations

Joey Fingold; Justin J. Slater

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arXiv · 2608.14898

Sequential Importance Sampling for Thinned Count Autoregressions via Latent Gaussian Transformations

Joey Fingold·Justin J. Slater

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Abstract

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.

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Joey Fingold, Justin J. Slater. 2026-08-14. Sequential Importance Sampling for Thinned Count Autoregressions via Latent Gaussian Transformations. https://arxiv.org/abs/2608.14898

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