I am looking for references that derive a Bayesian estimator for mutual information in the case of continuous data. My understanding is that this has been explored for discrete (e.g. Hutter, 2002, Archer et al., 2013) or mixed (Gao et al., 2017) data, but I'm struggling to find references for continuous data.
I can see that in this answer, for example, an approach to build an estimator using copulas is proposed. However, is it not Bayesian strictly speaking: ideally, I would like this credible interval to capture the finite number of samples, and come from a reasonable prior.
How can one estimate credible intervals of mutual information for continuous variables, even just for a bivariate distribution? If this has never been approached in the literature, is there an obvious reason why?
