Suppose we have a Markov chain with two states A
and B
.
This associated transition matrix is:
\begin{equation} P_{mc}= \begin{pmatrix} 0.3 & 0.7\\ 0.6 & 0.4 \end{pmatrix} \end{equation}
This matrix is empirical and computed from a set of observations:
e.g :A->B->A->A->A->B->A->A->B->B->A->B->B->A->B->A->B->A->B->B->B
My question is, After predicting a new state (B
or A
) how accurate is it to generate a new transition matrix P_mc
based on the new sequence and is there any theoretical limits to doing this?