% Online Bayesian model selection demo.% We generate data from the model A->B% and compute the posterior prob of all 3 dags on 2 nodes:%  (1) A B,  (2) A <- B , (3) A -> B% Models 2 and 3 are Markov equivalent, and therefore indistinguishable from % observational data alone.% We control the dependence of B on A by setting% P(B|A) = 0.5 - epislon and vary epsilon% as in Koller & Friedman book p512% ground truthN = 2;dag = zeros(N);A = 1; B = 2; dag(A,B) = 1;ntrials = 100;ns = 2*ones(1,N);true_bnet = mk_bnet(dag, ns);true_bnet.CPD{1} = tabular_CPD(true_bnet, 1, [0.5 0.5]);% hypothesis spaceG = mk_all_dags(N);nhyp = length(G);hyp_bnet = cell(1, nhyp);for h=1:nhyp  hyp_bnet{h} = mk_bnet(G{h}, ns);  for i=1:N    % We must set the CPTs to the mean of the prior for sequential log_marg_lik to be correct    % The BDeu prior is score equivalent, so models 2,3 will be indistinguishable.    % The uniform Dirichlet prior is not score equivalent...    fam = family(G{h}, i);    hyp_bnet{h}.CPD{i}= tabular_CPD(hyp_bnet{h}, i, 'prior_type', 'dirichlet', ...				    'CPT', 'unif');  endendclfseeds = 1:3;expt = 1;for seedi=1:length(seeds)  seed = seeds(seedi);  rand('state', seed);  randn('state', seed);      es = [0.05 0.1 0.15 0.2];  for ei=1:length(es)    e = es(ei);    true_bnet.CPD{2} = tabular_CPD(true_bnet, 2, [0.5+e 0.5-e; 0.5-e 0.5+e]);    prior = normalise(ones(1, nhyp));    hyp_w = zeros(ntrials+1, nhyp);    hyp_w(1,:) = prior(:)';    LL = zeros(1, nhyp);    ll = zeros(1, nhyp);    for t=1:ntrials      ev = cell2num(sample_bnet(true_bnet));      for i=1:nhyp	ll(i) = log_marg_lik_complete(hyp_bnet{i}, ev);	hyp_bnet{i} = bayes_update_params(hyp_bnet{i}, ev);      end      prior = normalise(prior .* exp(ll));      LL = LL + ll;      hyp_w(t+1,:) = prior;    end    % Plot posterior model probabilities    % Red = model 1 (no arcs), blue/green = models 2/3 (1 arc)    % Blue = model 2 (2->1)    % Green = model 3 (1->2, "ground truth")        subplot2(length(seeds), length(es), seedi, ei);    m = size(hyp_w,1);    h=plot(1:m, hyp_w(:,1), 'r-',  1:m, hyp_w(:,2), 'b-.', 1:m, hyp_w(:,3), 'g:');    axis([0 m   0 1])    %title('model posterior vs. time')    title(sprintf('e=%3.2f, seed=%d', e, seed));    drawnow    expt = expt + 1;  endend