Filtered sampling from populations with heterogeneous event frequencies

A hierarchical model is developed to account for selection biases that result from processes in which events have a fixed probability of being sampled, but individuals in the population generate events at varying rates. It is shown that inferences about the population parameters from such unrepresentative samples are not only possible but can be statistically powerful, provided the selection biases are adequately controlled for and the specification of the model is appropriate. The model assumptions are sufficiently flexible to accommodate a variety of stochastic processes with heterogeneous event frequencies. In an example, the model is applied to data on robbery rates for prison inmates in order to estimate the robbery rates for all offenders. The model fits the data well, and the results show that the bias toward high rate offenders among prison inmates is substantial.