How to generate a joint probability matrix from a data matrix

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.

Answer 1

[Michelangelo Ricciulli]

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.

Answer 2

[Roger Stafford]

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.