Using MLE's to create a Markov transition matrix
I was wondering if anyone knew how I could create a transition matrix for a Markov chain from a dataset. 2 examples of such data are attached. In the first example (in the first tab) a rabbit moves from one field to another across 7 months. How would I use MLE's to predict the transition probabilities in a transition matrix (with the current month being July)?
In this first example, there would be 3 fields A,B,and C.
In the second tab, there are also 3 fields, but there is a fourth state, D, which indicates that a particular rabbit has died. In this model there are also births. So given the current state, how could I then populate a transition matrix?
I do not want to include births in transition matrix. So ultimately with the second example, I would like to create a transition matrix to predict how many rabbits of the current population will be dead or in state A,B, or C by December (excluding any more births from August to December).
If I did want to allow for births as well, would this be a separate model? A Poisson process perhaps?
Any ideas are welcome.....(Wondering)