Hierarchical Bayesian Analysis of Arrest Rates

A Bayesian hierarchical model provides the basis for calibrating the crimes avoided by incarceration of individuals convicted of drug offenses compared to those convicted of nondrug offenses. Two methods for constructing reference priors for hierarchical models both lead to the same prior in the final model. We use Markov chain Monte Carlo methods to fit the model to data from a random sample of past arrest records of all felons convicted of drug trafficking, drug possession, robbery, or burglary in Los Angeles County in 1986 and 1990. The value of this formal analysis, as opposed to a simpler analysis that does not use the formal machinery of a Bayesian hierarchical model, is to provide interval estimates that account for the uncertainty due to the random effects.