A scalable Bayesian double machine learning framework, with application to racial disproportionality assessment

Racial disproportionality in stop and search practices elicits substantial concerns about its societal and behavioral impacts. In London, Black individuals are about four times more likely to be stopped and searched than White individuals. Using data on stop and search events in London from January 2019 to December 2023, this paper aims to investigate disproportionality in the volume of stops for expressive crimes involving Black individuals compared to other ethnicities. We employ a semi-parametric partially linear structural regression method and introduce a Bayesian empirical likelihood procedure combined with double machine learning techniques to control for high-dimensional confounding and to accommodate strong prior assumptions. In addition, we show that the proposed procedure yields a valid posterior in terms of coverage. Applying this approach to the stop and search dataset, we find that racial disproportionality aimed at the Black community may be influenced by the borough racial composition when focusing on expressive crimes.