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A transition matrix is a square matrix used to describe the transitions of a Markov chain.
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Accepted
Estimating Markov chain transition probabilities from data
Let $K$ be the number of states. The log-likelihood is
$$
\ell(p) = \sum_{i =1}^K \sum_{j =1}^K n_{ij} \log p_{ij}
$$
We now want to take the partial derivatives with respect to each $p_{ij}$, but rem …