If you have a binary sequence (e.g., converted from a large dataset like 2,678,400 values down to 744 binary values), and you'd like to compute Markov chain transition probabilities—specifically Pr(00), Pr(01), Pr(10), and Pr(11)—you can use the following MATLAB script:
% Initialization
count_00 = 0;
count_01 = 0;
count_10 = 0;
count_11 = 0;
% for loop to count the transitions
for i = 1:length(binary_seq) - 1
current = binary_seq(i);
next = binary_seq(i + 1);
if current == 0 && next == 0
count_00 = count_00 + 1;
elseif current == 0 && next == 1
count_01 = count_01 + 1;
elseif current == 1 && next == 0
count_10 = count_10 + 1;
elseif current == 1 && next == 1
count_11 = count_11 + 1;
end
end
% count the total transitions
total_transitions = count_00 + count_01 + count_10 + count_11;
% Compute probabilities
Pr_00 = count_00 / total_transitions;
Pr_01 = count_01 / total_transitions;
Pr_10 = count_10 / total_transitions;
Pr_11 = count_11 / total_transitions;
% display the results
disp(['Pr(00) = ' num2str(Pr_00)]);
disp(['Pr(01) = ' num2str(Pr_01)]);
disp(['Pr(10) = ' num2str(Pr_10)]);
disp(['Pr(11) = ' num2str(Pr_11)]);
The above script helps you compute the first-order Markov transition probabilities by analysing every pair of consecutive bits in your binary sequence.
