A colleague is conducting a Bayesian meta-analysis of some large-scale drug studies. Although she has experience with 'conventional' meta-analysis, she in new at the Bayesian approach. We have read several papers with related studies and approaches, and some authors report mean drug concentrations, while others report medians. Is one more appropriate than the other in the Bayesian context?
There is no single appropriate measure of central tendency in the Bayesian context. The measure you use depends on the research question and shape of the distribution. If your research question makes you want to know where the data splits into two parts of equal mass/density, AND your distribution is skewed, then use the median. If your research question is more about knowing the expected value of something because you are trying to maximize a utility function, and the expected utility hypothesis makes sense, then use the mean. If your posterior distribution is symmetric, it doesn't matter which one you use.