I am curious if there is a straightforward explanation for calculating the degrees of freedom of a hidden Markov model (HMM).
For example, take a simple HMM with a 1st-order Markov chain and 2 hidden behavioural states. The HMM is used to model the behavioural states giving rise to the movement patterns of a person walking on a hike. The 2 states are walking and resting, and can be described by the person's step lengths.
Thus, walking is characterised by medium to long step lengths and resting is characterised by short step lengths.
There are 1000 observations of the person walking (i.e. 1000 observations of step length).
Each state (walking and resting) has a gamma distribution (hence each state requires the estimation of a mean and standard deviation).
How would I calculate the degrees of freedom of such an HMM?