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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.

ThomasJohnson
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    You don't understand what [maximum likelihood](https://stats.stackexchange.com/questions/112451/maximum-likelihood-estimation-mle-in-layman-terms) is, or how was it calculated for the Markov chain? – Tim Nov 27 '17 at 16:29
  • 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 ? – ThomasJohnson Nov 27 '17 at 18:40
  • I know the answer very well, but do not have time to answer this right now. remember to ping me... – Haitao Du Nov 27 '17 at 20:44

1 Answers1

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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).

Zahava Kor
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  • 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 ? – ThomasJohnson Nov 27 '17 at 20:39