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Topic: Box & Tiao Equation
Replies: 0

 Paul M Booth Posts: 1 Registered: 12/18/04
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^2|sigma^2)=(1/(Gamma((1/2)*(n-1))*((n-1)/2*sigma^2)^((1/2)*(n-1)*
(s^2)^((1/2)*(n-1)-1)*exp(-(n-1)*s^2/2*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.

Can any help.

Thank you.

Paul Booth