diff --git a/prml_errata.tex b/prml_errata.tex index 805bde7..f1d1325 100644 --- a/prml_errata.tex +++ b/prml_errata.tex @@ -1971,18 +1971,20 @@ \subsubsection*{#1} (well approximated by the likelihood conditioned on $\mathbf{w}_{\text{ML}}$) so that the assumed model reduces to the least squares method, which is known to suffer from overfitting (see Section~1.1). + Of course, we can extend the model by incorporating hyperpriors over $\beta$ and $\alpha$, thus introducing more Bayesian averaging. However, if the extended model is not sensible (e.g., the hyperpriors are sharply peaked around wrong values), we shall again end up with a wrong posterior and a wrong predictive. -The point here is that, since we do not know the true model, +The point here is that, since we do not know the true model (if any), we cannot know whether the assumed model is sensible in advance -(i.e., without any knowledge about the data). -We can however assess whether a model is better than another -in terms of, say, \emph{Bayesian model comparison} (see Section~3.4), -though a caveat is that we still need some (implicit) assumptions for this procedure to work; +(i.e., without any knowledge about data to be generated). +We can however assess, given a data set, whether a model is better than another +by, say, \emph{Bayesian model comparison} (see Section~3.4), +though a caveat is that we still need some (implicit) assumptions for the framework of +Bayesian model comparison to work; see the discussion around (3.73). Moreover, one should also be aware of a subtlety here, that is,