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Math Help - How to get Transition matrix from input/output distributions???

  1. #1
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    How to get Transition matrix from input/output distributions???

    Hi,

    Can you solve this?

    [0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

    [0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

    [0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc
    (example made with real numbers)

    My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

    Any thoughts appreciated.
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  2. #2
    Super Member Anonymous1's Avatar
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    Quote Originally Posted by Trying View Post
    Hi,

    Can you solve this?

    [0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

    [0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

    [0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc
    (example made with real numbers)

    My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

    Any thoughts appreciated.
    \vec a \cdot B = \vec c

    \vec a^{-1} \cdot \vec a \cdot B = \vec a^{-1} \cdot  \vec c

    I \cdot B = \vec a^{-1} \cdot \vec c

    Just a thought...
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Trying View Post
    Hi,

    Can you solve this?

    [0.25 0.25 0.5][3x3 unknown transition matrix]=[0.2083 0.4167 0.3750]

    [0.2083 0.4167 0.3750][3x3 unknown transition matrix]=[0.2327 0.4757 0.2917]

    [0.2327 0.4757 0.2917][3x3 unknown transition matrix]=etc
    (example made with real numbers)

    My problem is I have a homogeneous Markov process (extremely large) that has the same transition matrix at every discrete time step. But the transition matrix was unknown. I have the input and output distributions at every time.

    Any thoughts appreciated.
    You have:

     <br />
\left[\begin{array}{ccc}<br />
0.25 & 0.25 & 0.5\\<br />
0.2083 & 0.4167 & 0.3750 \\<br />
0.2327 & 0.4757 & 0.2917<br />
\end{array}\right]\textbf{X}=<br />
\left[\begin{array}{ccc}<br />
0.2083 & 0.4167 & 0.3750\\<br />
0.2327 & 0.4757 & 0.2917 \\<br />
.. & .. & ..<br />
\end{array}\right]<br />

    So to find \textbf{X} you apply the inverse of the matrix multiplying it ..

    CB
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