A novel exploratory approach is developed to the analysis of a large table of counts. It uses random-effects models where the cells of the table (representing types of individuals) form the higher level in a multilevel model. The model includes Poisson variation and an offset to model the ratio of observed to expected values thereby permitting the analysis of relative rates. The model is estimated as a Bayesian model through MCMC procedures and the estimates are precision-weighted so that unreliable rates are down-weighted in the analysis. Once reliable rates have been obtained graphical and tabular analysis can be deployed. The analysis is illustrated through a study of the occupational class distribution for people of different age, birthplace-origin and generation in Australia. The case is also made that even where there is a full census there is a need to move beyond a descriptive analysis to a proper inferential and modelling framework. We also discuss the relative merits of Full and Empirical Bayes approaches to model estimation.