How to generate a joint probability matrix from a data matrix

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alpedhuez il 17 Mar 2018
Risposto: Roger Stafford il 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
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Michelangelo Ricciulli il 17 Mar 2018
Modificato: Michelangelo Ricciulli il 17 Mar 2018
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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Roger Stafford il 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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