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Re: Mathematica Integration help

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86165] Re: Mathematica Integration help
  • From: Francogrex <franco at grex.org>
  • Date: Tue, 4 Mar 2008 02:08:48 -0500 (EST)
  • References: <fqetdm$jjs$1@smc.vnet.net> <fqghgr$f65$1@smc.vnet.net>

On Mar 3, 10:48 am, antony.sea... at gmail.com wrote:
> What you're integrating doesn't make any sense as a statistical
> quantity.  Did you intend to have different mu_i and integrate over
> each such variable?  At the moment you're averaging the likelihood of
> {x_i} arising from Gaussians centred on the diagonal {mu, mu, mu, mu}
> for all mu.

Yes this is called the integrated likelihood. There is one mu, one
sigma and many x_i(s). The x_i(s) are the data. In classical MLE
estimation the mean(xbar)=sum(x_i)/n.
and the sigma (standard deviation) is sqrt[(sum (x_i - xbar)^2)/
(n-1)].
What we are trying here is elimination of the nuisance parameter (mu)
so that we can estimate sigma directly from the data (x_i). See
Reference:
Berger. Integrated Likelihood Methods for Eliminating Nuisance
Parameters. Statistical Science 1999, Vol. 14, No. 1, 1-28.


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