Bayes Factors using BIC statistic (model selection)


I need to compare four different models (logistic regression), model selection is performed using bayes factors using the BIC statisic.

BIC can be transformed to the probability of the data given a model:

PrBIC(D|Hi) = exp[-BIC(Hi)/2]

And so, we can compute the Bayes factors:

BF01 = (PrBIC(D|H0))/(PrBIC(D|H1) = exp[deltaBIC10/2]

with deltaBIC10 = BIC(H1)-BIC(H0).

However, I need to perform model selection on four predefined (logistic regression) models.Literature also tells that if we have multiple competing models we can compute the a posterior probability for each of these models given the data as follows:

PrBIC(Hi|D) = (exp[-0.5BIC(Hi)]) / (Sum(exp[-0.5BIC(Hj))

What's wisedom here? Calculate each BF against each model apart (model 1 against model 2, if evidence is in favor of model 1, than check model 1 with model 3, and so on). Or, calculate the posterior probabilty for competing models and than translate it to a new Bayes factor...Or is my last point just wrong?