def _messages_backwards_log_fast(trans_potential, init_potential, likelihood_log_potential_llt):
errs = np.seterr(over='ignore')
Al = np.log(trans_potential)
pil = np.log(init_potential)
aBl = likelihood_log_potential_llt
nhs = trans_potential.shape[0]
sequence_length = aBl.shape[0]
betal = np.zeros((sequence_length, nhs * 2))
giant_Al_pil = np.tile(np.vstack((np.tile(pil, (nhs,1)), Al )), (1,2))
for t in xrange(betal.shape[0]-2,-1,-1):
np.logaddexp.reduce( giant_Al_pil + betal[t+1] + aBl[t+1], axis=1, out=(betal[t]))
np.seterr(**errs)
return betal
### Gibbs sampling
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