When possible, the frequentist will restrict attention to a low-dimensional statistic which is a sufficient statistic for the unknown parameter(s) of the model.

Having adopted a specific probability model for the data and reduced the data via sufficiency, the frequentist statistician would then seek to identify an estimator of the unknown parameter(s) having some desirable (frequency-based) performance properties. Regarding the modeling of the data and the possible data-reduction via sufficiency, the Bayesian and the frequentist approaches are identical. At this point, however, the Bayesian statistician takes off in a markedly different direction.