Normalising likelihood for BIC/AIC calculation I am running some model inference using AIC and BIC. My problem is that when I go and calculate the (maximum) loglikelihoods of my models, they are usually really high (range between 4700 and 1400 approx.).
This is mostly because I have a lot of data points, in the order of 20k, and (apparently) decently good models. So the likelihood for each individual point is often > 1 and the sum of their logs is positive and gets quite high.
Now, if I use these values to calculate BIC and AIC and from there the posterior probabilities of my model, I often get a numerical error, because I have very negative BIC/AIC ($<-1000$) and the number I'd get with $\exp(-0.5\text{BIC})$ is just too big for R. This is also the case when I use $\text{BIC}-\text{BIC}_{max}$.
I am considering using normalised likelihood instead of likelihood (i.e. $1/N\cdot \text{likelihood}$). How does this (and sample size in general) affect BIC/AIC and model inference methods? I couldn't really find anything useful to read about this.

Lower BIC scores are better, so the normalised value you're supposed to use is $\Delta BIC = BIC - BIC_{\text{min}}$, not max (see this paper, which shows the calculations for AIC, but the BIC equations are the same and this is easier to find).
With that done, your highest BIC will be $0$, everything else will be positive, and the $w_{BIC} = exp(-.5\Delta BIC)$ term will work as expected.
