'Intractable and unsolved': some thoughts on statistical data assimilation with uncertain static parameters

If you seem to be able to do data assimilation with uncertain static parameters then you are probably not working in environmental science. In this field, applications are often characterized by sensitive dependence on initial conditions and attracting sets in the state-space, which, taken together, can be a major challenge to numerical methods, leading to very peaky likelihood functions. Inherently stochastic models and uncertain static parameters increase the challenge.