Introduction of pests and diseases through trade is one of the main socio-ecological challenges worldwide. Although Binomial sampling inspection at the border can reduce pest entry risk, it is common for consignments to fail inspection, wasting resources for both exporter and importer. Outsourcing the inspection to the exporting country could reduce the cost of inspection for both parties. However, there is then a need to assess the quality of the offshore inspection. In this paper, we develop an inverse method combining past inspection data on the pathway, an onshore inspection sample, and the Beta-Binomial model to infer the sample size of the offshore inspection. We illustrate the method on two case studies: the importation of live plants through germplasm into Australia and the importation of pelleted seeds in New Zealand. In these case studies, we found that detecting four to five infested units in a single onshore inspection was typically sufficient to significantly doubt the presence of a compliant offshore inspection. We also ran a simulation experiment to quantify the statistical power to reject or accept the presence of compliant offshore inspection in practice: In highly infested pathways, we could detect the absence of offshore inspections after inspecting five consignments onshore. Less infested pathways required inspecting 20 to 60 consignments onshore. Our study demonstrates that Binomial sampling onshore can be used to assess the quality of offshore inspections.
Keywords: Bayesian inference; Beta-Binomial; border biosecurity; conjugate prior; empirical Bayes method; inspection; inverse modeling; quality control; quarantine; species invasion.
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