how to automatically calculate probalities of a long binary sequence ?

hello ,

i have a matlab data (2678400 values (seconds)) , converted to a binary sequence of 744 values of 0s and 1s . i need to calculate 4 probabilities (markov chain 4 states ) Pr(11),Pr(10),Pr(01),Pr(00) is there a code that can do that ?

thanks

Answer 1

[TARUN]

Hi @Lina Hadjar Ferhat,

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.