Hi Vijay,
Assuming you already have an observed sequence of states 'X' and a known number of unique states 'S', you can build a Markov Chain transition probability matrix using MATLAB math functionalities like 'zeros': https://www.mathworks.com/help/matlab/ref/zeros.html
The idea is to count how often each transition from state 'i' to state 'j' occurs and then normalize it to get probabilities. Here's a simple implementation:
function P = buildMarkovChain(X, S)
Nij = zeros(S, S); % Counts of transitions from state i to state j
Ni = zeros(1, S); % Counts of transitions starting from state i
for t = 1:length(X)-1
i = X(t);
j = X(t+1);
Nij(i, j) = Nij(i, j) + 1;
Ni(i) = Ni(i) + 1;
end
% Transition probability matrix
P = zeros(S, S);
for i = 1:S
if Ni(i) > 0
P(i, :) = Nij(i, :) / Ni(i); % Normalize row i to get probabilities
end
end
end
Each row of the resulting matrix 'P' gives the probability distribution of transitioning from a given state to all possible next states. The logic inside the loop builds a frequency count for transitions, and the second loop turns those counts into probabilities using basic element-wise operations.
Hope this helps!
