When it comes to dealing with real data, it is important that one accounts for model uncertainty. As famously pointed out by the British statistician George Box:
“All models are wrong, but some are useful.” – George Box
Sure, but which ones are useful? To answer this question, one needs to take into account model uncertainty in their estimation problems. Under model uncertainty, one assumes that the observed data could have been generated according to multiple candidate models, with the goal of learning the joint posterior distribution over the models and their corresponding unknown parameters. For dynamically evolving systems, model uncertainty becomes even more complicated, since models (or regimes) can change over time. For example, in the well-known problem of tracking a maneuvering target, the best representative model depends on the target’s trajectory, which changes over time.
One of the goals of my research is to develop principled ways for accounting for model uncertainty in complex systems. I am most interested in regime switching systems, i.e., systems for which the best representative model can change over time.