Thread: 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.

Originally Posted by Trying

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.

Just a thought...

Originally Posted by Trying

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:



So to find you apply the inverse of the matrix multiplying it ..

CB