A Bayesian Framework for Estimating the True Incidence of Gender-Based Violence in Italy

Under-reporting severely affects the measurement of gender-based violence, where official statistics capture only a small share of actual incidents. This paper develops a hierarchical Bayesian framework that integrates individual-level survey data with region-level administrative counts to estimate the true incidence of violence against women in Italy. The approach addresses three challenges: the latent nature of true event counts, the mismatch between macro-area survey data and regional aggregates, and ecological bias arising from the divergence between individual-level relationships and aggregated covariate means. Individual-level information on both experiencing the event and reporting it is used to estimate covariate-specific risks and reporting probabilities, which are then transferred to the regional level. A compound PoissonBinomial structure models under-reporting while allowing partial pooling across regions. The empirical application highlights marked regional disparities and the severity of hidden incidence.