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A Normal Approximation to N-mixture Models with Applications in Large Abundance Estimation and Disease Surveillance Public Deposited

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  • N-mixture models provide a structure for making inference about a local population size while accounting for imperfect detection. Using a binomial likelihood, they assume prior distributions on the size parameters and then integrate those parameters out of the full likelihood. For large population sizes, the established frequentist methods have exhibited computational intractability, and the Bayesian methods have exhibited poor convergence and mixing of chains. Additionally, estimability of parameters in these types of models has been criticized in the literature. Although originally used for determining abundance of rare wildlife, we explore using these models for under-diagnosed or under-ascertained infectious diseases which have large prevalence. We derive an asymptotic approximation of the N-mixture model that does not suffer from computational efficiency and uses information theory to provide a method for diagnosing estimability issues. Additionally, we extend this model to account for spatial dependency. Simulation studies show improved performance over the established methods in numerous settings, and we successfully apply the asymptotic approximation to model ten years of Oregon Health Authority chlamydia data.
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