Re: Mathematica Integration help

*To*: mathgroup at smc.vnet.net*Subject*: [mg86177] Re: Mathematica Integration help*From*: Mark Fisher <particlefilter at gmail.com>*Date*: Wed, 5 Mar 2008 03:38:13 -0500 (EST)*References*: <fqetdm$jjs$1@smc.vnet.net> <fqghgr$f65$1@smc.vnet.net>

On Mar 4, 2:15 am, Francogrex <fra... at grex.org> wrote: > 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. First, you need to compute the definite integral, {\[Mu], -Infinity, Infinity}. (Use GenerateConditions -> False or Assumptions -> \[Sigma] > 0.) Second, I don't think Mathematica will compute the integral for the symbolic product, so you will have to give a specific value to n. Third, you will have to make the substitution of xbar yourself. --Mark