Analysis of Arrest Rates

Subir Sinha

Abstract:

We investigate the offenses committed by felons in the United States (U.S.). The two counties that we consider are Los Angeles (California) and Maricopa (Arizona). The data were collected from convicted felons in the above mentioned two counties during 1986 and 1990. The primary aim of the proposed analysis is to compare arrest rates of different kinds of offenders to assess the crime control potential associated with recent increases in drug offenders within the criminal justice system. The statistical analysis for addressing this issue involves a Bayesian analysis in which the posterior distribution cannot be obtained in closed form and we use instead Markov chain simulation, which produces a sequence of random variables distributed approximately from the posterior distribution. These random variables can be used to estimate the posterior or features of it like the posterior expectation and variance. In addition to the arrest rates of offenders, there are other covariates which we incorporate through model selection and use them to fit a general regression model. Again the posterior cannot be obtained in closed form and so we use Metropolis within Gibbs to get the posterior of the regression coefficients corresponding to the previously selected covariates which answers some more questions of interest.

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