0
$\begingroup$

could anyone please give me intuitive explanation what does below mean ?

Let say I have sequence: a, b, a, b, b, b, a, b, b, a

By applying Markov Chains with MLE method in R package on below I get transition matrix and log likelihood as per below: a b a 0.0 1.0 b 0.5 0.5

log likelihood of -4.158883

I understand how to compute transition matrix. But I don't seem to understand log likelihood.

Could somebody please intuitively explain to me what this represents on above example ?

Many thanks.

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ You don't understand what maximum likelihood is, or how was it calculated for the Markov chain? $\endgroup$
    – Tim
    Commented Nov 27, 2017 at 16:29
  • $\begingroup$ Unfortunately I still don't understand how does that apply on Markov Chains and how exactly I can represent this log likelihood of -4.158883. Can you please advise on that ? $\endgroup$
    – ThomasJohnson
    Commented Nov 27, 2017 at 18:40
  • $\begingroup$ I know the answer very well, but do not have time to answer this right now. remember to ping me... $\endgroup$
    – Haitao Du
    Commented Nov 27, 2017 at 20:44

1 Answer 1

Reset to default
1
$\begingroup$

Your sequence a, b, a, b, b, b, a, b, b, a has a combined probability (or likelihood) which is the product of all the one-step transition probabilities of the sequence: a->b, b->a, a->b, b->b, and so on until the final b->a (9 transitions in total). If you multiply these 9 probabilities based on your table you get 1/64. This is the likelihood (probability) of your sequence. The natural logarithm (base e) of 1/64 is -4.158883. 1/64 happens to be the maximum combined transition probability for your given sequence out of all possible combinations of one-step transition probabilities for the chain, and therefore -4.158883 is the maximum logarithm of this combined probability (likelihood).

Improve this answer
$\endgroup$
1
  • $\begingroup$ Thank you, it's more clear now. One more question, if I say that my likelihood is 1/64 can I assume out of that if the Markov Chain is a good model for the data ? Or this has nothing to do with it ? Does this tell me, that there is 1/64 probability that this sequence will repeat based on transition table ? $\endgroup$
    – ThomasJohnson
    Commented Nov 27, 2017 at 20:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.