Results 1 to 5 of 5

Thread: Interpretation of the fundamental matrix of Absorbing Markov Chain

  1. #1
    Newbie
    Joined
    Dec 2017
    From
    Belgium
    Posts
    3

    Interpretation of the fundamental matrix of Absorbing Markov Chain

    Hello!

    I am studying the Absorbing Markov Chain theory, and I have a question about how to interpret the fundamental matrix (N). It is defined as the average number of times transient state j is encountered in the transition from transient state i to an absorbing state, but many times the values of N are not integer numbers. So, how should I interpret a N values of 0.2 or 1.8 for example? Should I just round it to the nearest integer? I have read many examples but in non of them this fraction number are explained.

    Thanks for your help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,779
    Thanks
    3028

    Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

    Can you give an example of a problem in which the entries of such a matrix are not non-negative integers? If it were not for that "1.8" I would suspect that the entry in the "i,j" position is the probability of transition from state i to state j rather than the "number of times" the transition occurs.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2017
    From
    Belgium
    Posts
    3

    Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

    Thanks for your answer, but no, this matrix gives the number of times a state is reached, and it is based on the transition matrix that gives the probability of the change of state.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2017
    From
    New York
    Posts
    16
    Thanks
    4

    Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

    Margodoy, you said yourself: "the average number of times". Averages (expectations) are rarely round numbers. If the expectation is 0.2, then the interpretation is: in most random scenarios there is 0 or 1 visit to transient state j before absorption, with the probability of 0-visit scenarios being roughly 80%. As uninspiring as this statement is, there is nothing more to say.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2017
    From
    Belgium
    Posts
    3

    Re: Interpretation of the fundamental matrix of Absorbing Markov Chain

    Thanks a lot
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Absorbing Markov Chain
    Posted in the Statistics Forum
    Replies: 1
    Last Post: Oct 31st 2012, 05:14 PM
  2. Replies: 2
    Last Post: Sep 21st 2012, 07:53 AM
  3. Replies: 3
    Last Post: Sep 20th 2012, 08:54 PM
  4. Replies: 0
    Last Post: Apr 15th 2012, 10:41 PM
  5. Markov Chain - Transition Matrix
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Apr 9th 2009, 02:51 PM

Search Tags


/mathhelpforum @mathhelpforum