%
% Example on epage 445 
% 
% Problem on epage 471
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');

randn('seed',0); rand('seed',0); 

% Get the variances for the proposal distributions.
sigs = 0.5*ones(3,1); 
% We will generate 500 iterations of the chain.
n = 500;
% Set up the vectors to store the samples.
X = zeros(3,n); 

% Get the starting values for the chains.
X(1,1) = -25; 
X(2,1) = -15; 
X(3,1) =  -5; 

fh=figure; lt = {}; 

for nc=1:3,
  % Run each chain:
  X1 = X(nc,:); 
  for i = 2:n
    % Generate variate from proposal distribution.
    y = randn(1)*sigs(nc) + X1(i-1);
    % Generate variate from uniform.
    u = rand(1);
    % Calculate alpha.
    alpha = normpdf(y,0,1)/normpdf(X1(i-1),0,1);
    if u <= alpha
      % Then set the chain to the y.
      X1(i) = y;
    else
      X1(i) = X1(i-1);
    end
  end
  X(nc,:) = X1;
  lt{nc} = ['X(0) = ',num2str(X(nc,1))]; 
end

figure(fh); hold on; ph=[];
ph(end+1)=plot( X(1,:), 'rx-' ); ph(end+1)=plot( X(2,:), 'gx-' ); ph(end+1)=plot( X(3,:), 'x-k' ); grid on; 
xlabel('iteration value'); ylabel('X(i)'); 
title( 'MC Chain as a function of different starting values' ); 
legend( ph, lt, 'location', 'southeast' ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter11/prob_11_4_chain_w_diff_starts', 'epsc' ); 

clear functions;