CHAPTER 34 – Bayesian inversion of dynamic models

In this chapter, we look at the inversion of dynamic models. We use, as an example, the haemodynamic model presented in Chapter 27. The inversion scheme is an extension of the Bayesian treatments reviewed in Part 4. Inverting haemodynamic models of neuronal responses is clearly central to functional magnetic resonance imaging (fMRI) and forms the basis for dynamic causal models for fMRI based on neuronal networks (see Chapter 41). However, the principles of the inversion described in this chapter can be applied to any analytic, deterministic dynamic system and we will use exactly the same scheme for dynamic models of magnetoen-cephalography/electroencephalography (M/EEG) later. In this chapter, we focus on the inversion of a single model to find the conditional density of the model's parameters that can then be used for inference, on parameter space. In the next chapter, we will focus on inference about models themselves (i.e. inference on model space), in terms of Bayesian model comparison, selection and averaging.