Individuals engage in criminal careers which are treated as stochastic processes governed by fixed parameters (e.g., a rate parameter), and these parameters come from specified distributions. The parameters of these distributions at the upper level of the hierarchy must then be specified. The models are estimated using data on all persons arrested at least once in the six-county Detroit Standard Metropolitan Statistical Area during the four years 1974-1977 for a criterion offense (an index crime other than larceny) and arrested at least once for robbery through April 1979. There is a bias toward selecting those with a higher arrest frequency. In order to make more general inferences, statistical adjustment was needed to overcome the arrest-frequency sampling bias. We construct a series of models for the arrest career and fit the models with the data set of arrests. After correcting biases in the data, we estimate the model parameters using empirical Bayes methods and then examine the resulting models. 6 tables, 4 notes, 1 appendix, 14 references. (Author abstract)