Mauch MIREX 2010

function pi = sum_prod_CPD_and_pi_msgs(CPD, n, ps, msg, except)

% SUM_PROD_CPD_AND_PI_MSGS Compute pi = sum_{u\p} P(n|u) prod_{ui in ps\p} pi_msg(ui->n)

% pi = sum_prod_CPD_and_pi_msgs(CPD, n, ps, msg, p)

%

% pi  = prod_i (qi pi_msg(ui->n) + 1 - pi_msg(ui->n)) = prod_i (1 - ci pi_msg(ui->n))

% is the product of the endorsement withheld (Pearl p188 eqn 4.56)

% We skip p from this product, if specified.

if nargin < 5, except = -1; end

pi = 1;

for i=1:length(ps)

  p = ps(i);

  if p ~= except

    pi_from_parent = msg{n}.pi_from_parent{i};

    q = CPD.inhibit(i);

    c = 1-q;

    pi = pi * (1 - c*pi_from_parent(2));

  end

end

% The pi msg that a leak node sends to its child is [0 1]

% since its own pi is [0 1] and its lambda to self is [0 1].

q = CPD.leak_inhibit;

% 1 - c*pi_from_parent = 1-c*1 = q

pi = pi * q;