simulate a markov chain including the absorbing state "death"
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Sehrish Usman
il 25 Gen 2021
Commentato: Sehrish Usman
il 25 Gen 2021
I am simulating a Markov chain process with the transition probability matrix:
P = [0.9044 0.0099 0 0 0.0857;...
0 0.7287 0.1057 0.0799 0.0857;...
0 0.0699 0.8183 0 0.1118; ...
0 0.376 0 0.6199 0.0041; ...
0 0 0 0 1]
where I have five states = single, marriage, divorce, widow and death
When I run the simulations, I always end up with state 5 (which is death).
Should I not include the abosrbing state?
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John D'Errico
il 25 Gen 2021
Modificato: John D'Errico
il 25 Gen 2021
You won't always eventually die? While there are ways for that to not happen eventually, usually they are the plot of some movie. And if you DO know some way to avoid that particular absorbing state, you might consider selling the formula. my guess is there would be a few buyers at any cost.
Seriously, all states eventually allow transition into the absorbing state with some non-zero probability, so the long time state of the system would have you always in the absoring state. This is just an expected behavior for such a process.
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John D'Errico
il 25 Gen 2021
I'm not sure what you are asking. Are you saying that you do not know how to generate a viable transition matrix from data, say from marriage, and death statistics? Or are you talking about a formulation of such a process in the form of a system of ordinary differential equations, where now you would have a death rate, marriage rate, etc., each of which would depend on the state you are currently in.
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