Increasingly we use machine learning to build interactive systems that learn from past actions and the reward obtained. Theory suggests several possible approaches, such as contextual bandits, reinforcement learning, the do-calculus, or plain old Bayesian decision theory. What are the most theoretically appropriate and practical approaches to doing causal inference for interactive systems? We are particularly interested in case studies of applying machine learning methods to interactive systems that did or did not use Bayesian or likelihood based methods, with a discussion about why this choice was made in terms of practical or theoretical arguments.