help needed to make transition probability matrix

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Mahesh
Mahesh 2015-7-27
评论： Mahesh 2015-7-27
Dear all, I am brainstorming how to make transition probability matrix and had a code below. It does not work. It could be great to check my code and have a idea so that sum of all values in the matrix shall be one. My mind blocked after thinking a lot.
A = idxMA;
nmax = max(A);
nseries = numel(A);
states = zeros(nseries, nmax);
for i = 1:nmax
states(:,i) = A==i;
end
jumpprob = zeros(nmax);
jmps = 1:nmax;
for i = 1:nmax
X = jmps(i);
for j = 1:njumps
Y = jmps(j);
P = jumps(A, X, Y);
jumpprob(i,j) = P/nseries;
end
end
function [ P ] = jumps(data, X, Y )
%UNTITLED5 Summary of this function goes here
% Detailed explanation goes here
ndata = length(data);
nstates = 0;
for i = 1:ndata-1
if data(i) > X && data(i+1) <= Y
nstates = nstates + 1;
end
end
P = nstates;
end

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John D'Errico
John D'Errico 2015-7-27
Um, no. A transition matrix does NOT have the sum of ALL values in the matrix as 1.
It must have the sum of every ROW of the matrix 1. There is a big difference. So as written below, T would be a valid transition matrix.
n = 6;
T = rand(n,n);
T = bsxfun(@times,T,1./sum(T,2))
T =
0.19273 0.06588 0.22642 0.1874 0.16056 0.16702
0.24566 0.14832 0.13164 0.26023 0.20551 0.0086335
0.035665 0.26892 0.22476 0.18417 0.20871 0.077775
0.36619 0.38684 0.056885 0.014318 0.15725 0.018511
0.22476 0.056021 0.14991 0.30181 0.23298 0.034524
0.02493 0.24807 0.23405 0.23872 0.043754 0.21047
The sum of the probabilities to move from any given state to one of the other states must be 1. So the sum of each row is 1, as I said it must be.
sum(T,2)
ans =
1
1
1
1
1
1
  2 个评论
Mahesh
Mahesh 2015-7-27
Well thanks for the clue. But I am having problem with calculating matrix T. For that I have data
A = [2 2 2 2 2 2 7 7 7 7 7 7 7 7 7 4 4 4 4 4 4 10 10 10 10 1 1 1 1 1 6 6 5 5 5 9 9 9 9 9 9 9 9 3 3 3 3 9 3 3 8 8 8 8 8]
I hope it works for you to make me clear
Mahesh
Mahesh 2015-7-27
Moreover I got the matrix with all elements of last row is zeros. I tested with other set same thing happens.
jumpprob = [
12 18 21 22 31 36 45 49
7 13 16 17 25 30 39 43
3 9 12 13 21 25 33 37
3 4 7 8 16 20 28 31
3 4 5 6 14 18 25 28
3 4 4 4 12 16 23 26
3 3 3 3 3 7 14 17
3 3 3 3 3 3 10 13
1 1 1 1 1 1 1 4
0 0 0 0 0 0 0 0]
I hope you may get the mistake thanks

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