Bayes Factor Calculation

[O Allicock]

Hi All,
A technical question regarding BEAST. For comparing models using the
Bayes Factor, the website says: "...by calculating the harmonic mean
of the likelihood from the posterior output of each of the models and
then taking the difference (in log space) you get the log BF and you
can look up this number in a table to decide when the BF (log BF) is
big enough to strongly favour one model over the other". Does this
"table" just refer to log tables? I assume we just have to find the
inverse log? Or is there some other table?
And when it says BF(logBF) I assume those brackets mean one or the
other and not the product of the two?

Thanks
Orchid

[alexei....@gmail.com]

Hi Orchid,

When people talk about Bayes factors, they are always talking about
the ratio of the marginal likelihoods of the the two models, however
they can refer to this ratio in a number of different units. Two such
units are natural units and log units (others things like decibans are
also used). I have previously suggested that a BF >20 is strong
evidence supporting the preferred model (The interpretation of this is
that the preferred model supports the data 20 time more than the other
model)

There is a table at http://en.wikipedia.org/wiki/Bayes_factor which
suggests that a BF of 10-30 is Strong, 30-100 is very strong and >100
is Decisive. In log BF (natural log) this would be:

log BF Strength of evidence
2.3-3.4 Strong
3.4-4.6 Very Strong
>4.6 Decisive

Since the harmonic mean estimator of the marginal likelihood
frequently has errors on the order of 1 log unit, only decisive BF and
greater can really be relied on (What I really mean by this is that
you must take into account the errors associated with estimating a BF
when interpreting it).

Cheers
Alexei