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Edit: A Bayesian model that exhibits overfitting (#10)
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yousuketakada committed Apr 7, 2018
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Expand Up @@ -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,
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