Sampling, inference and dynamical systems

Apart from the common challenges of dealing with explosive growth in data, there are several other key difficulties peculiar to dynamical systems, such as the lack of explicit forms of likelihood and complicated dependence structures among data.

The problems without explicitly specified likelihoods fall into two categories. In the first category, the likelihood can be made available in analytical forms if we embed the problem in an appropriately augmented space. Such data augmentation schemes typically rely on MCMC algorithms and on related tools, such as approximate Bayesian computation. In the second category, the model is a “black box,” and we only have a generating stochastic mechanism to simulate data from the model. An appropriate framework for addressing such problems is based on the idea of indirect inference and auxiliary variable methods.