wolffd@0: function marginal = marginal_family(engine, i, t)
wolffd@0: % MARGINAL_FAMILY Compute the marginal on the specified family (ff)
wolffd@0: % marginal = marginal_family(engine, i, t)
wolffd@0: 
wolffd@0: if nargin < 3, t = 1; end
wolffd@0: 
wolffd@0: % The method is similar to the following HMM equation:
wolffd@0: % xi(i,j,t) = normalise( alpha(i,t) * transmat(i,j) * obsmat(j,t+1) * beta(j,t+1) )
wolffd@0: % where xi(i,j,t) = Pr(Q(t)=i, Q(t+1)=j | y(1:T))
wolffd@0: 
wolffd@0: bnet = bnet_from_engine(engine);
wolffd@0: 
wolffd@0: if myismember(i, engine.onodes)
wolffd@0:   ps = parents(bnet.dag, i);
wolffd@0:   p = ps(1);
wolffd@0:   marginal = pot_to_marginal(engine.marginals{p,t});
wolffd@0:   marginal.domain = [p i];
wolffd@0:   return;
wolffd@0: end
wolffd@0: 
wolffd@0: if t==1
wolffd@0:   marginal = pot_to_marginal(engine.marginals{i,t});
wolffd@0:   return;
wolffd@0: end
wolffd@0: 
wolffd@0: bnet = bnet_from_engine(engine);
wolffd@0: ss = length(bnet.intra);
wolffd@0: pot = engine.CPDpot{i,t};
wolffd@0: c = engine.obschild(i);
wolffd@0: pot = multiply_by_pot(pot, engine.CPDpot{c,t});
wolffd@0: pot = multiply_by_pot(pot, engine.back{i,t});
wolffd@0: ps = parents(bnet.dag, i+ss);
wolffd@0: for p=ps(:)'
wolffd@0:   pot = multiply_by_pot(pot, engine.fwd{p,t-1});
wolffd@0: end
wolffd@0: marginal = pot_to_marginal(normalize_pot(pot));
wolffd@0: 
wolffd@0: