% EXAMPLE2.m

% -------------------------------------------

% Introduction to inference using Bayes' rule

% Learning about a student's ability

% [from Albert (1996), p. 29]



% Here the models are the ability levels of the student ("good",

% "mediocre" and "poor") and the data are the possible grades

% in a course ("A", "B", "C", "D", "F").  You observe the 4 grades

% B, B, C, C and wish to compute the probabilities of the ability

% levels.



prior = [.6

         .3

         .1];                 % initial probabilities of the three models

      

like = [.4 .4 .2  0  0

        .1 .2 .4 .2 .1  

         0  0 .3 .5 .2];      % likelihoods of 5 grades for each model

      

data = [2 2 3 3];             % observed test result

     

post = bayes(prior,like,data) % computes matrix of posterior probabilities 

                              % of the three models -- the first row

                              % contains the updated probabilities after observing

                              % the first grade, the second row contains the

                              % probabilities after observing the first two grades,

                              % etc.

     

     