Where do priors and causal models come from? An experimental design perspective

In this pedagogical note, we treat prior elicitation and experimental design within a common decision making framework. This is contrary to the standard practice of assuming that priors are already available when performing Bayesian experimental design. We argue instead that these processes are intertwined. We demonstrate our decision-theoretic stance in the setting of learning a causal Bayesian network prior sequentially. We choose among a set of actions (consulting an expert, observing more data and conducting interventions and experiments) to maximize the gain in information.