Hi it occurred to me that for numerical stability people often use the log-likelihood instead of a real pdf/likelihood. And while this might work fine for MAP & MLE it's not obvious that it works for true Bayesian Inference (e.g. MCMC) since it isn't technically proportional to the real pdf.
Now image you have a dataset $D$ of size $|D|>100$ so the likelihood multiplies 100+ pdf values: $L(D|\theta)=\prod^{|D|}_ip(D_i|\theta)$... Does that cause problems?
