function [fwd, loglik] = filter_evidence(engine, CPDpot, observed, pot_type)% [fwd, loglik] = filter_evidence(engine, CPDpot, observed, pot_type) (ff)[ss T] = size(CPDpot);fwd = cell(ss,T);hnodes = engine.hnodes(:)';onodes = engine.onodes(:)';bnet = bnet_from_engine(engine);ns = bnet.node_sizes;onodes2 = [onodes onodes+ss];ns(onodes2) = 1;logscale = zeros(1,T);H = length(hnodes);local_logscale = zeros(1,ss);  t = 1;for i=hnodes  fwd{i,t} = CPDpot{i,t};  c = engine.obschild(i);  if c > 0    fwd{i,t} = multiply_by_pot(fwd{i,t}, CPDpot{c, t});  end  [fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});endlogscale(t) = sum(local_logscale);for t=2:T  for i=hnodes    ps = parents(bnet.dag, i+ss);    assert(all(ps<=ss)); % in previous slice    prior = CPDpot{i,t};    for p=ps(:)'      prior = multiply_by_pot(prior, fwd{p,t-1});    end    fwd{i,t} = marginalize_pot(prior, i+ss);    fwd{i,t} = set_domain_pot(fwd{i,t}, i);    c = engine.obschild(i);    if c > 0      fwd{i,t} = multiply_by_pot(fwd{i,t}, CPDpot{c,t});    end    [fwd{i,t}, local_logscale(i)] = normalize_pot(fwd{i,t});  end  logscale(t) = sum(local_logscale);endloglik = sum(logscale);