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How to generate a joint probability matrix from a data matrix

Asked by alpedhuez on 17 Mar 2018
Latest activity Answered by Roger Stafford on 17 Mar 2018
Suppose I have a data matrix
Sample# X Y
1 1 1
2 1 2
3 1 1
Then I want to generate a joint prob matrix
X Y Prob
1 1 0.67
1 2 0.33
Please advise.

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2 Answers

Answer by Michelangelo Ricciulli on 17 Mar 2018
Edited by Michelangelo Ricciulli on 17 Mar 2018
 Accepted Answer

Hi, A simple way to get the joint probability matrix for two dimension is using the hist3 function, (read the documentation here ). Let's call your initial matrix nXY
nXY=[1 1 1;
2 1 2;
3 1 1]
You will need only the last two columns to count the occurrence of each combination of X and Y (So, we can use nXY(:,2:3)). Also, you need to define a cell array containing all the possible X values and Y values. In this case, just 1 and 2, so:
Xv=[1 2];
Yv=[1 2];
values={Xv Yv};
count=hist3(nXY(:,2:3),'ctrs',values); %first count the values
p=count/sum(sum(count)); % then divide by the sum on all matrix value to get probability
You will get in the estimated joint probabilities in the matrix p. You'll just need to rewrite them in the form you need.

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Answer by Roger Stafford on 17 Mar 2018

Call the data matrix D. Then the two columns of D(:,2:3) are X and Y.
XY = sortrows(D(:,2:3));
F = find( [true,any(XY(1:end-1,:)~=XY(2:end,:),2),true] );
J = [XY(F(1:end-1),2:3),diff(F)/(F(end)-1)]; % <-- Joint probabilities in column 3
Columns 1 and 2 of J will contain unique X Y pairs.

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