1

If I know for a fact that event A happens 21 times before event B happens, and B then happens 7 times before event A and the cycle repeats,

Can I say that the probability of the B happening after event A is 7/28 and event A happening after event A is 21/28 just for the purpose of expressing the problem as a Hidden Markov Model problem?

I want to apply Hidden Markov Model to my problem but in the textbooks, they just assume we are dealing with probabilities, but in my real-world problem, it's not a probability, this cycle is a certainty. Can I still use HMM for my real-world use case?

TSR
  • 507
  • If you know for a fact that... then there is no discrete range of probabilities, only the boolean true or false. After three A's f.e., probability for A is 1 and for B is 0. – Piita Apr 16 '23 at 01:46
  • Perhaps I am mistaken. I am totally ignorant of Markov Theory. The way that I interpret the question, once you are given that event $~A~$ has just happened, there are $~21~$ equally likely possibilities. That is, it must be that event $~A~$ has just happened $~k~$ consecutive times, where $~k \in {1,2,\cdots,21}.~$ Therefore, the probability of $~B~$ immediately happening is $~\frac{1}{21}.$ – user2661923 Apr 16 '23 at 04:03
  • Another way of thinking about the same thing is that you imagine that there are $~28~$ places around a circular table, $~21~$ consecutive $~A$'s, $~$ followed by $~7~$ consecutive $~B$'s. $~$ When you know that $~A~$ has just happened, all that this tells you is that you have eliminated $~7~$ of the $~28~$ equally likely positions around the table that you might be located. – user2661923 Apr 16 '23 at 04:06

0 Answers0