Contents

coin_scenario1.m

From A First Course in Machine Learning, Chapter 2. Simon Rogers, 01/11/11 [simon.rogers@glasgow.ac.uk] Coin game, prior scenario 1

clear all;close all;

Load the coin data

load ../data/coin_data

Plot the prior density

alpha = 1;
beta = 1;
fprintf('\nPrior parameters: alpha: %g, beta: %g',alpha,beta);
r = [0:0.01:1];
plot(r,betapdf(r,alpha,beta));
xlabel('r');
ylabel('p(r)');

Prior parameters: alpha: 1, beta: 1

Incorporate the data one toss at a time

post_alpha = alpha;
post_beta = beta;
ch = {'T','H'};
toss_string = [];
for i = 1:length(toss_data)

   toss_string = [toss_string ch{toss_data(i)+1}];
   figure(1);hold off
   plot(r,betapdf(r,post_alpha,post_beta),'k--');
   post_alpha = post_alpha + toss_data(i);
   post_beta = post_beta + 1 - toss_data(i);
   hold on
   plot(r,betapdf(r,post_alpha,post_beta),'k');
   legend('Previous posterior','New posterior');
   ti = sprintf('Posterior after %g tosses: %s',i,toss_string);
   title(ti);
   xlabel('r');ylabel('p(r|...)');

end

Incorporate another ten

figure(1);hold off
plot(r,betapdf(r,post_alpha,post_beta),'k--');
hold on
N = length(toss_data2);
post_alpha = post_alpha + sum(toss_data2);
post_beta = post_beta + N - sum(toss_data2);
plot(r,betapdf(r,post_alpha,post_beta),'k');
legend('Posterior after 10','Posterior after 20');
xlabel('r');ylabel('p(r|...)');

Incorpoate another 1000

figure(1);hold off
plot(r,betapdf(r,post_alpha,post_beta),'k--');
hold on
N = length(big_data);
post_alpha = post_alpha + sum(big_data);
post_beta = post_beta + N - sum(big_data);
plot(r,betapdf(r,post_alpha,post_beta),'k');
legend('Posterior after 20','Posterior after 1020');
xlabel('r');ylabel('p(r|...)');

Interactive example

fprintf('\n Enter H or T to add a toss result and see the effect on the posterior.  Use ctrl-C to exit');
nTosses = 0;
post_alpha = alpha;
post_beta = beta;
close all;
while 1
    fprintf('\nYou have currently entered %g tosses\n',nTosses);
    this_toss = input('Enter next toss (H or T):','s');
    figure(1);hold off
    plot(r,betapdf(r,post_alpha,post_beta),'k--');
    hold on
    switch this_toss
        case 'H'
            post_alpha = post_alpha + 1;
        case 'T'
            post_beta = post_beta + 1;
        otherwise
            fprintf('\n Please enter H or T');
            continue
    end
    nTosses = nTosses + 1;
    plot(r,betapdf(r,post_alpha,post_beta),'k');
    legend('Previous','New');
end

 Enter H or T to add a toss result and see the effect on the posterior.  Use ctrl-C to exit
You have currently entered 0 tosses

Error using ==> input
Cannot call INPUT from EVALC.

Error in ==> coin_scenario1 at 69
    this_toss = input('Enter next toss (H or T):','s');

Published with MATLAB® 7.12