how to programme in Matlab to obtain transition probability matrix?
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I have a sequence x= [12,14,6,15,15,15,15,6,8,8,18,18,14,14] so I want to make transition probability matrix. Transition probability matrix calculated by equation i.e. probability=(number of pairs x(t) followed by x(t+1))/(number of pairs x(t) followed by any state). Matrix should be like below
6 8 12 14 15 18
6 0 1/2 0 0 1/2 0
8 0 1/2 0 0 0 1/2
12 0 0 0 1 0 0
14 1/2 0 0 1/2 0 0
15 1/4 0 0 0 3/4 0
18 0 0 0 0 1/2 1/2
by following code I can do
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;
but with this code matrix forms of order maximum state present in sequence i.e. matrix becomes of 18*18, and much more places zero occurs. I want matrix like above posted by me how to do it.
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