## How to generate a joint probability matrix from a data matrix

### alpedhuez (view profile)

on 17 Mar 2018
Latest activity Answered by Roger Stafford

### Roger Stafford (view profile)

on 17 Mar 2018
Accepted Answer by Michelangelo Ricciulli

### Michelangelo Ricciulli (view profile)

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

### Products ### Michelangelo Ricciulli (view profile)

Answer by Michelangelo Ricciulli

### Michelangelo Ricciulli (view profile)

on 17 Mar 2018
Edited by Michelangelo Ricciulli

### Michelangelo Ricciulli (view profile)

on 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. ### Roger Stafford (view profile)

Answer by Roger Stafford

### Roger Stafford (view profile)

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.