Given a list of log-likelihood $\log\mathcal{L}_i$ for $ i \in [1, N]$, if I want to compute the average log-likelihood correctly, I need
$$ \langle \log \mathcal{L} \rangle = \log\left(\frac{1}{N}\sum_{i=1}^{N}e^{\log\mathcal{L}_i}\right).$$ (taking the mean of the logs themselves is not the same).
However, for large likelihoods I quickly run into numerical problems (the reason for using log-likelihoods in the first place..)
Is there any methods to improve the numerical stability? Or am I missing something here...
