I would like to compare the correlation coefficients from two different models of the same data points. One of them is the raw bivariate data (Value vs Time), and the other is given a biologically-motivated modification (modified value vs time), which I would like to show increases the R^2. You can compare Fisher transforms of R as in https://seriousstats.wordpress.com/2012/02/05/comparing-correlations/, but this is not Bayesian, which would be more consistent with the rest of the paper.
I've seen a few articles on Bayesian inference of Pearson correlation (http://www.sumsar.net/blog/2013/08/bayesian-estimation-of-correlation/), but am not sure how to compare them for data sets that are not independent. My understanding is that some form of the variance sum law could be used to account for dependence. Any suggestions would be awesome.