Random variables have a prior distribution and a posterior distribution. Denote the prior by bi (for ``before") and posterior by ai (for ``after"). Define pi=ai/bi, and insert pi in any of the inequalities above. Now suppose we have an adjustable model parameter upon which the ai all depend. Suppose we adjust that model parameter to try to make some Jensen inequality into an equality. Thus we will be adjusting it to get all the pi equal to each other, that is, to make all the posteriors equal to their priors. It is nice to have so many ways to do this, one for each Jensen inequality. The next question is, which Jensen inequality should we use? I cannot answer this directly, but we can learn more about the various inequalities.