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.