For this function of the 3R + 2 emission parameters , a and b we now find the maximum likelihood estimates using the Newton-Raphson iteration method. We may do this by taking the explicit derivatives of the likelihood function, possible because of the simple substitution model used. If we had opted for a more complicated model, we would need optimization methods that did not rely on derivatives and would subsequently be slower, though the estimation would still be possible. Once the change in log-likelihood between two iterations has fallen below some given threshold, we take the likelihood to have converged. We then generate a new emission matrix E to be fed back into our alignment procedure in order to generate new posterior probabilities.