Dear Connie,
both, the log-evidence and the posterior probability, indicate the
relative strength of the respective model compared to all other models
within the model space. The posterior probability is simply the
probability of the model given the data under the additional assumption
that at least one suitable (hopefully the true) model is included in
your model space. This last assumption is easy to see when you sum up
the posteriors across the whole model space which always will amount to
one.
While the log-evidence is hard (if at all) to interpret the posterior
probability is much more intuitive to understand. Nevertheless the
posterior probability is a conditional one that presupposes the data.
Therefore, the posteriors can only be compared within the same data set.
Moreover, as already indicated indirectly above, BMS can only search
within the model space that you defined. It is not able to search im- or
explicitly beyond that space.
Best wishes,
Thilo
On Mon, 2013-12-02 at 17:39 +0000, Connie Luu wrote:
> Dear all,
>
> I was wondering if someone could explain what log evidence and model posterior probability mean, and what are the units of measurement? From my understanding, log evidence is the relative likelihood of a model compared to other models within the same dataset only, whereas model posterior probability may be compared between models of different datasets - is that correct?
>
> Thanks,
> Connie
>
> --
> Connie Luu
> Undergraduate Student
> University of Alberta
>
>
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