# Difficulties when implement Bayesian information Criterion (BIC)

I was reading some papers related to Bayesian model selection.

The Bayesian information criterion (BIC) model selection criterion is given by $$\text{BIC}=-2\log f({\bf y}|\hat{\theta})+p\log n$$ where $$p$$ is the dimension of the model parameter $$\theta$$, and $$n$$ is the sample size.

In non-i.i.d settings, like mixed model for clustered data or autoregression model for longitudinal data, the sample size $$n$$ in BIC criterion is not well defined.

There are some papers I was reading talking about using the inverse of the information matrix (or similar method) to get the effective sample size $$n_e$$, however, in practice or in some programming package that implements BIC, the sample size is still used either as the total sample size $$n$$, or the number of subjects $$N$$.

I was wondering what is the difficulties in implementation of BIC? If the effective sample size could be well defined as in those papers, why we do not use it widely?