Why is the $1-\alpha$ Bayesian credible interval for $\lambda \sim \chi^2_{v}$ have endpoints $\chi^2_{v, 1-\alpha/2}$ and $\chi^2_{v,\alpha/2}$? Suppose that a posterior distribution $\lambda$ has distribution $\lambda \sim \chi^2_{v}$. 
Then, it is often written that a $1-\alpha$ Bayesian credible interval for $\lambda \sim \chi^2_{v}$ will have have lower and upper endpoints of $\chi^2_{v, 1-\alpha/2}$ and $\chi^2_{v,\alpha/2}$, respectively. I am wondering why the lower endpoint starts at $1-\alpha/2$ instead of $\alpha/2$? If $\alpha = 0.05$, then it seems weird for the lower point to start at $\chi^2_{v, 1-0.05/2} = \chi^2_{v, 0.975}$, which is the UPPER endpoint of a frequentist interval. Thanks.

 A: The OP has added the excerpt from the Casella-Berger book.  It shows that the authors agree with the points I made about credible regions and confidence intervals.  It clears up all my issues and answers all the questions I wrote in the comments. The answer boils down to the fact that the resulting posterior distribution is chi-square with 14 degrees of freedom.  Casella and Berger made the endpoints of the credible region unique by requiring equal probability alpha/2 ( 0.05 in the example) to be below the lower endpoint and above the upper endpoint. In a standard statistic textbook, I found that the endpoints given by Casella and Berger in the example agree exactly with the table.
Here is the key point that clears up the confusion. The simple explanation is that the points in the table correspond to the area to the right of that point. Hence 0.95 in the example for the lower endpoint and 0.05 for the upper endpoint. So Casella and Berger's notation is consistent with the chi-square table.
