Sequential Importance Sampling for Thinned Count Autoregressions via Latent Gaussian Transformations

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.