I have a training set of sequences. I want to reach a discrete time Markov model (transition probability matrix).

Is there a Bayesian way other than MLE to achieve this?

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    $\begingroup$ Short answer: yes. But we'll probably need more information about your specific case to give any meaningful advice. $\endgroup$ – Maurits M Jul 18 at 21:14
  • $\begingroup$ Thanks! So I have a dataset consists of user navigation on a website. Each item is a sequence of the user's page hits. And I'd like to create a markov model from the data using Bayesian approach. My question is how do I formulate the model? For example, what would be the prior and how to write down likelihood. $\endgroup$ – Bruce Jeaung Jul 19 at 9:16
  • $\begingroup$ It would probably make sense to expand your question to include this information. I don't have much experience with this kind of use case, but you want to estimate the probability of moving from one page to the next. The 'simple' MLE estimate is just the proportion of times a user moves from a given page to each other page. You can introduce prior information in that users might follow a specific pattern, or that links might be displayed in a specific order. Describing this in formulas might be challenging (or impossible if you don't have the right data). Hope this helps! $\endgroup$ – Maurits M Jul 22 at 8:11

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