calculation of the transition probability of a Markov's chain

Hi all

 I have to series of data (i.e. Qt and Qt+1 , in t and t+1 times, respectively). I want to  calculate the transition probability of P[Qt+1 | Qt] that called first order transition probability of a Markov chain.

How can I do this.

cheers

Answer 1

[Walter Roberson]

allstates = unique([Qt(:); Qt1(:)]);
[TF, fromstate_num] = ismember(Qt, allstates);
[TF, tostate_num] = ismember(Qt1, allstates);
went_from_to_count = accumarray( [fromstate_num(:), tostate_num(:)], 1, []);
num_trans_away_from = min(1, sum(went_from_to_count, 2));
went_from_to_prob = went_from_to_count ./ repmat( num_trans_away_from, 1, size(went_from_to_count,2) );

After this,

went_from_to_prob(J,K) is P[allstates(K) | allstates(J)]

Note that an entire row could be empty, if the last state transitioned to does not otherwise occur (the "accept" state.)