  The use of cash bail as a mechanism for detaining defendants pre-trial is an
often-criticized system that many have argued violates the presumption of
"innocent until proven guilty." Many studies have sought to understand both the
long-term effects of cash bail's use and the disparate rate of cash bail
assignments along demographic lines (race, gender, etc). However, such work is
often susceptible to problems of infra-marginality -- that the data we observe
can only describe average outcomes, and not the outcomes associated with the
marginal decision.
  In this work, we address this problem by creating a hierarchical Bayesian
model of cash bail assignments. Specifically, our approach models cash bail
decisions as a probabilistic process whereby judges balance the relative costs
of assigning cash bail with the cost of defendants potentially skipping court
dates, and where these skip probabilities are estimated based upon features of
the individual case. We then use Monte Carlo inference to sample the
distribution over these costs for different magistrates and across different
races. We fit this model to a data set we have collected of over 50,000 court
cases in the Allegheny and Philadelphia counties in Pennsylvania. Our analysis
of 50 separate judges shows that they are uniformly more likely to assign cash
bail to black defendants than to white defendants, even given identical
likelihood of skipping a court appearance. This analysis raises further
questions about the equity of the practice of cash bail, irrespective of its
underlying legal justification.
