How do I solve this conditional probabilities problem with MATLAB?

Question

If P( c _j | x _i ) are already known, where i=1,2,...n; j=1,2,...k;

How do I calculate/estimate: P( c _j | x _l , x _m , x _n ) , where j=1,2,...k; l,m,n belongs to http://latex.mathoverflow.net/jsMath/fonts/cmsy10/alpha/120/char32.png {1,2,...n} ?

Answer 1

EDIT2 (following the OP's comment)

From bayes rule we know that P(C|x1,x2,x3) ~ P(C)*P(x1,x2,x3|C) and therefore for classification, you compute that expression for all C=j and predict the most likely class ( MAP ).

Now to compute P(x1,x2,x3|C) , for iid observations, this can be written as: P(x1,x2,x3|C) = P(x1|C)*P(x2|C)*P(x3|C) , which given a parametric model each could be computed easily.

Answer 2

Maybe this site can help? I'm assuming your trying to implement the Bayes rule in Matlab.

Answer 3

What you want to do is not possible without further information or simplifying assumptions.

The conditional probability P(A|B,C) is not (completely/at all :) determined by P(A|B) and P(A|C).