How do I interpret negative BIC scores?

[abul]

Dear Hugin Support,

The more I read about BIC on the internet, the more I get confused. Some say we have to choose the model with highest BIC score and some say lowest BIC score.

Which one is right?

Also, how do I interpret negative BIC scores (which I generally get in the Hugin models learned through EM algorithm)? Which one is better: -100 or -200? Also, which one is better: 100 or 200?

Please reply to clear this confusion.

Regards,

Abul

[Anders L Madsen]

Hi Abul,

In the discrete case, the BIC score can only be negative. It is defined as (see section 11.2 of the HUGIN C API Reference Manual):

l-1/2*k*log (n)

where l is log-likelihood, k is the number of free parameters, and n is the number of cases.

When comparing two models with different BIC scores, you should select the one with the highest score (e.g., if the scores are -100 and -200, then the highest score is -100).

You can read about the BIC score here: http://en.wikipedia.org/wiki/Bayesian_information_criterion

In the continuous case, i.e., for CG networks,  the log-likelihood is computed from the value of the density at the observed value. This may produce a positive contribution to the log-likelihood.

Hope this helps.

[Flore]

Dear Hugin Support,
I send you this message just to be sure of something.
You say in your message that "When comparing two models with different BIC scores, you should select the one with the highest score (e.g., if the scores are -100 and -200, then the highest score is -100)"
And on the wiki link you mentioned we can read "Given any two estimated models, the model with the lower value of BIC is the one to be preferred".
So I just want to be sure that I have to use the model with the BIC highest score.
Thanks for the answer
Regards,
Flore

[Anders L Madsen]

As far as I can tell the difference is that the BIC score used in HUGIN is the negation of the BIC score defined on the wiki. This means that in HUGIN you should be maximizing the model scores whereas using the BIC score as defined on the wiki you should be minimizing the score.

Thus, in HUGIN you should select the model with the highest score (and "-100> -200").