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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?

Lzz0
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  • What have you tried so far? Take a look on [How to ask a good question in Stack Overflow](https://stackoverflow.com/help/how-to-ask) and [How to create a minimal, complete, and verifiable example](https://stackoverflow.com/help/mcve). – Matheus Portela Apr 19 '18 at 18:04
  • Basically, I am looking for the appropriate way to solve this rather than coding. But I am struggling with it. – Lzz0 Apr 19 '18 at 18:38
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    In this case, it is more appropriate to place your question at [Cross Validated](https://stats.stackexchange.com/), where people will be able to discuss the proper approach. Here, in Stack Overflow, we are focused in programming questions & answers. – Matheus Portela Apr 20 '18 at 13:52
  • I am also thinking so. Thank you for your suggestion – Lzz0 Apr 20 '18 at 17:20

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