\HeaderA{estimateSigmaMV}{Fit zero mean multivariate t-distribution}{estimateSigmaMV}
\keyword{htest}{estimateSigmaMV}
\keyword{models}{estimateSigmaMV}
\keyword{design}{estimateSigmaMV}
\begin{Description}\relax
estimate the parameters \eqn{\Sigma}{Sigma}, m and \eqn{\nu}{v} of the multivariate t-distribution with zero expectation.
\end{Description}
\begin{Usage}
\begin{verbatim}
estimateSigmaMV(y,maxIter=100,epsilon=0.000001,verbose=FALSE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{y}] data matrix
\item[\code{maxIter}] maximum number of iterations
\item[\code{epsilon}] convergence criteria
\item[\code{verbose}] print computation info or not
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The multivariate t-distribution is parametrized as:
\deqn{y|c \sim N(\mu,c\Sigma)}{y|c ~ N(mu,c*Sigma)}
\deqn{c \sim \mbox{InvGamma}(m/2,m\nu/2)}{c ~ InvGamma(m/2,m*v/2)}
Here \eqn{N}{N} denotes a multivariate normal distribution, 
\eqn{\Sigma}{Sigma} is a covariance matrix and 
\eqn{\mbox{InvGamma}(\alpha,\beta)}{InvGamma(a,b)} is the inverse-gamma distribution with density function
\deqn{f(x)=(\beta)^{\alpha} \exp\{-\beta/x\} x^{-\alpha-1}/\Gamma(\alpha)}{f(x)=b^a exp\{-b/x\} x^{-a-1} /Gamma(a)}
In this application \eqn{\mu}{mu} equals zero, and m is the degrees of freedom.
\end{Details}
\begin{Value}
\begin{ldescription}
\item[\code{Sigma}] Estimated covariance matrix for y
\item[\code{m}] Estimated shape parameter for inverse-gamma prior for gene variances
\item[\code{v}] Estimated scale parameter for inverse-gamma prior for gene variances
\item[\code{converged}] T if the EM algorithms converged
\item[\code{iter}] Number of iterations
\item[\code{modS2}] Moderated estimator of gene-specific variances
\item[\code{histLogS2}] Histogram of log(s2) where s2 is the ordinary variance estimator
\item[\code{fittedDensityLogS2}] The fitted density for log(s2)
\end{ldescription}
\end{Value}
\begin{Author}\relax
Magnus \eqn{\mbox{\AA}}{A}strand
\end{Author}
\begin{References}\relax
Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.

Kristiansson, E., Sj\eqn{\mbox{\"o}}{o}gren, A., Rudemo, M., Nerman, O. (2005). Weighted Analysis of Paired Microarray Experiments. Statistical Applications in Genetics and Molecular Biology 4(1)

\eqn{\mbox{\AA}}{A}strand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.

\eqn{\mbox{\AA}}{A}strand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.
\end{References}
\begin{SeeAlso}\relax
estimateSigma
\end{SeeAlso}

