% See www.cs.berkeley.edu/~murphyk/Bayes/usage.html for details.N = 4; dag = zeros(N,N);dag(1,2) = 1; dag(1,3) = 1; dag(2,4) = 1; dag(3,4) = 1;ns = 2*ones(1,N);bnet = make_bnet(dag, ns);bnet.CPD{1} = tabular_CPD(bnet, 1, [0.5 0.5]);bnet.CPD{2} = tabular_CPD(bnet, 2, [0.8 0.2 0.2 0.8]);bnet.CPD{3} = tabular_CPD(bnet, 3, [0.5 0.9 0.5 0.1]);bnet.CPD{4} = tabular_CPD(bnet, 4, [1 0.1 0.1 0.01 0 0.9 0.9 0.99]);evidence = cell(1,N);evidence{2} = 2;query = [2 3 4];% Enumerationengine1 = enumerative_inf_engine(bnet);[m1, ll1] = infer(engine1, evidence, query);%p1 = m1.T(2)%assert(approxeq(p1, 0.4298))% variable eliminationengine2 = var_elim_inf_engine(bnet);[m2, ll2] = infer(engine2, evidence, query);approxeq(m1.T, m2.T)approxeq(ll1, ll2)% jtreeengine3 = jtree_inf_engine(bnet);[marginals3, fmarginals3, ll3] = infer(engine3, evidence);m3 = marginals3{query};approxeq(m1.T(:), m3.T(:))approxeq(ll1, ll3)% BNTbnet0 = mk_bnet(dag, ns);for i=1:N  bnet0.bnodes{i} = mk_tabular_node(bnet0,i);endbnet0.bnodes{1}.CPT(:) = [0.5 0.5];bnet0.bnodes{2}.CPT(:) = [0.8 0.2 0.2 0.8];bnet0.bnodes{3}.CPT(:) = [0.5 0.9 0.5 0.1];bnet0.bnodes{4}.CPT(:) = [1 0.1 0.1 0.01 0 0.9 0.9 0.99];obs_nodes = [4];vals = [2];[bnet0, ll0] = enter_evidence(bnet0, vals, obs_nodes);m0 = marginal_nodes(bnet0, query);approxeq(m0.T, m1.T)approxeq(ll0, ll1)   % marginal on hidden and observed nodesquery = [3 4];% since node 4 is instantiated to 2,% m1(x3,x4) will be 0s except where x4 = 2[m1, ll1] = infer(engine1, evidence, query);[m2, ll2] = infer(engine2, evidence, query);assert(approxeq(m1.T, m2.T))m0 = marginal_nodes(bnet0, query);assert(approxeq(m1.T, m0.T))