I am trying to do some self study of Bayesian statistical techniques and have encountered a difficulty. I trying to understand where equation 1.4.12 in Box & Tiao 'Bayesian Inference in Statistical Analysis' came from.
The equation is the sampling distribution of s^ conditioned on sigma^2:
and is said (suggested) in the text to come from "(n-1)*s^2 is distributed as sigman^2*Chi^2".
I would expect that one would simply substitute (n-1)*s^2/sigma^2 in the chi-square distribution to get the above result. My results for this substitution is close to the above. The difference is a factor of 1/2 and a -1 in the first exponent. This is close enought to suggest that there may have been an error in the type setting.
I am using computer algebra and taking other precautions to ensure against an algebra error myself.
Another explanation is this equation comes from somewhere else and I am completely befuddled.