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What is the effect of increasing or decreasing the number of states in markov chain process ?

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  • $\begingroup$ Could you be more precise ? Increasing or decreasing number of states could modify the reductibility of the chain, the period of existing states, the mean recurrence... well approximately everything. $\endgroup$ – lcrmorin Mar 26 '13 at 17:42
  • $\begingroup$ @Imorin I am using markov chain for prediction. I am clustering data to get the states of the markov chain process. Can increase or decrease of states can change the transition matrix's accuracy ? If I have any wrong concept about it please correct me. $\endgroup$ – Diptopol Dam Mar 26 '13 at 18:10
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The coefficients of the transition matrix gives the probability to change from a state to another. So if you add a state, first you will add a dimension, so yes, the transition matrix is changed. Then, as you add a state (and a state probably linked to other state) this will also modify the coefficient of the previous matrix.

If you are asking about the efficience of your algorithm, answer is yes too. Think about the algorithm of the k-means, used to cluster datas. If k, the number of groups, is too low, you won't see anything. If k is too big, you will see many uninteresting things.

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  • $\begingroup$ @Imorin Then what should be my approach to maintain a standard in selecting the number of states in markov chain process. $\endgroup$ – Diptopol Dam Mar 26 '13 at 23:30
  • $\begingroup$ @Imorin I had another question stackoverflow.com/questions/15656270/… . If you have any experience working with that please help me out or if you any site where I can get help please share with me. :) $\endgroup$ – Diptopol Dam Mar 27 '13 at 10:43
  • $\begingroup$ There is probably a mathematical way to select the number of states, but I'm not aware of them. I only know about some indicators as Mean square errors. The best advice I can give to you is to work with different number of states. You will be able to select the best numbers of states with your results. $\endgroup$ – lcrmorin Mar 27 '13 at 10:59
  • $\begingroup$ sorry I changed my link stats.stackexchange.com/questions/53425/… $\endgroup$ – Diptopol Dam Mar 27 '13 at 11:01

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