Biotic invasions threaten global biodiversity and ecosystem function, and present challenges to agriculture where invasive pest species require major economic investment in control and can cause significant production losses. Pest Risk Analysis (PRA) is key to prioritizing agricultural biosecurity efforts, but is hampered by incomplete knowledge of current crop pest and pathogen distributions. Here we develop predictive models of current pest distributions and test these models using new observations at sub-national resolution. We apply generalized linear models (GLM) to estimate presence probabilities for 1901 crop pests in the CABI pest distribution database. We test model predictions for 100 unobserved pests in the Peoples Republic of China (PRC), against observations of these pests abstracted from the Chinese literature which has hitherto been omitted from databases on global pest distributions. Finally, we predict occurrences of all unobserved pests globally. Presence probability increases with host presence, presence in neighbouring regions, and global prevalence, and decreases with mean distance from coast, per capita GDP, and host number. The models are good predictors of pest presence in Provinces of the PRC, with AUC values of 0.76 - 0.80. Large numbers of currently unobserved, but probably present pests, are predicted in China, India, southern Brazil and some countries of the former USSR. GLMs can predict presences of pseudo-absent pests at sub-national resolution. Controlling for countries scientific capacity improves model fit. The Chinese scientific literature has been largely inaccessible to Western academia but contains important information that can support PRA. Prior studies have often assumed that unreported pests in a global distribution database is a true absence. Our analysis provides a method for quantifying pseudo-absences to enable improved PRA and species distribution modelling.