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Box & Tiao Equation
Posted:
Jul 2, 1996 9:22 AM


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:
p(s^2sigma^2)=(1/(Gamma((1/2)*(n1))*((n1)/2*sigma^2)^((1/2)*(n1)* (s^2)^((1/2)*(n1)1)*exp((n1)*s^2/2*sigma^2)
and is said (suggested) in the text to come from "(n1)*s^2 is distributed as sigman^2*Chi^2".
I would expect that one would simply substitute (n1)*s^2/sigma^2 in the chisquare 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.
Can any help.
Thank you.
Paul Booth



