In this paper we show that an identification criterion inspired by the behavioural framework can be related in a very direct way to more traditional identification criteria. Specifically, we consider maximum a posteriori identification and symmetric instrumental variable methods. The behavioural criterion is studied in a traditional identification framework, and we do make an a priori partitioning of the observed data into inputs and outputs. Nevertheless, the behavioural criterion does look quite different to existing schemes. However, by making certain approximations in some cases, we show how these schemes are related.