Thus we see that there are very close similarities between this Bayesian viewpoint and the conventional one
based on error function minimization and regularization, since the latter can be obtained as a specific approximation
to the Bayesian approach. However, there is also a key distinction which is that in a Bayesian treatment we make
predictions by integrating over the distribution of model parameters w, rather than by using a specific estimated value
of w. On the one hand such integrations may often be analytically intractable and require either sophisticated Markov
chain Monte Carlo methods, or more recent deterministic schemes such as variational techniques, to approximate them.
On the other hand the integration implied by the Bayesian framework overcomes the issue of over-fitting (by averaging over
many different possible solutions) and typically results in improved predictive capability.