Suppose I have a transition matrix like this:
A B C
A 0.2 0.3 0.5
B 0.8 0.1 0.1
C 0.3 0.3 0.4
I can get the log likelihood of this by the following formula:
$L_{mc}=\sum_{i=1}^M\sum_{j=1}^M.N_{ij}.ln(T_{ij})$
If I have a new sequence like A, A, B, A, C, C, A
, How can I calculate the log-likelihood of the new sequence based on the above transition probability?