how to programme to calculate transition probability matrix?
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Suppose I have a sequence of states like 1,3,3,1,2,1,4,2,3,1,4,2,4,4,4,3,1,2,5,1. Transition probability matrix calculated by following equation probability=(number of pairs x(t) followed by x(t+1))/(number of pairs x(t) followed by any state). transition probability matrix calculated by manually by me as follows
1 3 2 4 5
1 0 1/5 2/5 2/5 0
3 3/4 1/4 0 0 0
2 1/4 1/4 0 1/4 1/4
4 0 1/5 2/5 2/5 0
5 1 0 0 0 0
how to programme to obtain above transition probability matrix.
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Answers (1)
James Tursa
on 5 May 2016
Edited: James Tursa
on 5 May 2016
E.g., brute force:
m = max(x);
n = numel(x);
y = zeros(m,1);
p = zeros(m,m);
for k=1:n-1
y(x(k)) = y(x(k)) + 1;
p(x(k),x(k+1)) = p(x(k),x(k+1)) + 1;
end
p = bsxfun(@rdivide,p,y); p(isnan(p)) = 0;
The p matrix will be ordered by natural indexing. E.g., 1, 2, 3, 4, 5 for the above example. It will not be ordered as 1, 3, 2, 4, 5 as you have it above. I.e., the probability of going from state i to state j is p(i,j).
4 Comments
Patrick Laux
on 10 Nov 2018
Edited: Patrick Laux
on 10 Nov 2018
The brute force code above is giving 5 if you sum up all probabilities ??
Shouldn't it be: p = bsxfun(@rdivide,p,n) ?
However, this, i.e. sum(sum(p)) also gives only 0.95 (not 1). I am confused now.
Maybe: p = bsxfun(@rdivide,p,n-1) ??
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