function y = cross_val(c,obs)
%% c is the point being left out, obs is the observations

%% cross validation.
%% omit one point, estimate the paras, then estimate the point using the
%% parameters. Easy case to include, leave out the first observation and
%% see what happens. May not be the best one to start with since it should
%% carry alot of weight. 
clear i k samples s_r expected_fails variance_fails recreatd
point_left_out=c;
basics_f

%just to be sure, re sample points from the prior.
%run sampling_f
display('sampling from prior (again)')
sampling_f
% now compute the weights associated with each point. 

display('compute the weights for these prior samples')
for k=1:KK
    l_weight(k)=0;
    %re calculate the failure rate
    s_r = samples(k,2) + samples(k,1)*exp(-samples(k,3).*(0:I));    %compute the failure rate for the sampled values FOR ALL POINTS INCLUDING THE ONE ASSOCIATED WITH THE POINT OMMITTED
    s_r = samples(k,2) + samples(k,1)*exp(-samples(k,3).*(0:I));    %compute the failure rate for the sampled values 
    expected_fails = expected_function(samples(k,1),samples(k,2),samples(k,3));
    variance_fails = variances_func(samples(k,1),samples(k,2),samples(k,3));
    index=1;
    for i=2:I   %first obs is zero since components are working when they are produced.
        if i==point_left_out %% ESSENTIALLY, WHAT THIS IS DOING IS COMPUTING THE WEIGHTS THE EXACT SAME WAY BUT IGNORING THE EFFECT THAT POINT 'c' HAS
            index=index+1;
              else
            l_weight(k) = l_weight(k) + log_pnorm(obs(i),expected_fails(i),variance_fails(i));
        end
    end
end

clear s_r expected_fails variance_fails k
display('computing weights')
maxt = max(exp(l_weight));
maxt = log(maxt);
for k=1:KK
    temp1(k) = l_weight(k) - maxt;
    temp2(k) = exp(temp1(k));
end
temp3 = sum(temp2);
temp4 = maxt+log(temp3);
s=exp(temp4);

for k=1:KK
    weight(k) = exp(l_weight(k))/s;
end
clear temp1 temp2 temp3 temp4 l_weight maxt
s_cdf=cumsum(weight);

for i=1:MM
    u=rand(1);  
    sample_x = 1;
        while (u > s_cdf(sample_x))
            sample_x=sample_x+1;
        end
    posterior_sim_cross(i,:)=samples(sample_x,:);
end

clear sample_x u i 

%% Now, have sampled from the posterior but omitted one point. 
%% Now, recreate that point using the estimated values of the parameters.
p
x_post_sim_cross = mean(posterior_sim_cross);
display('cross val values')
x_post_sim_cross
recreatd = expected_function(x_post_sim_cross(1),x_post_sim_cross(2),x_post_sim_cross(3));
var_recreatd = variances_func(x_post_sim_cross(1),x_post_sim_cross(2),x_post_sim_cross(3));
display('obs(c) - expected value 2*SD')
[obs(point_left_out) recreatd(point_left_out) 2*sqrt(var_recreatd(point_left_out))]

y=recreatd(point_left_out);