Integrating multiple tests Bayes factors

Question

I have been using an Bayesian-centric R package for some genomics analysis to detect mutations in 3 individuals from the same family.

I have to do each analysis for each individual separately due to how the package is written. All 3 individuals test positively when I apply the Bayesian test, and I get a Bayes factor of say 4, 7 and 9 for the three separate tests, which is in the realms of 'substantial' evidence as far as I can tell (e.g. http://en.wikipedia.org/wiki/Bayes_factor#Interpretation)

My question is, as these 3 individuals all carry the mutation (which was also our prior hypothesis), can I integrate these independently tested Bayes factors to provide a sort of 'meta-analysis' Bayes factor, which would presumably be > 10 for the whole family?

Answer 1

The short answer is no. In a sense, a Bayes factor is equivalent to BIC:

http://www.stat.sc.edu/~hitchcock/stat535slidesday21.pdf

Therefore, your question is similar to asking whether it's possible to figure out BIC for the "global" model that includes all individuals if one knows the three BICs produced by the individual models. Apparently, you'll have to fit the "global" model explicitly for that.

You may be able to analyze the entire dataset with your package by introducing a dummy variable for the individual.