plw (version 1.30.0)

estimateSigmaMV: Fit zero mean multivariate t-distribution

Description

estimate the parameters $Sigma$, m and $v$ of the multivariate t-distribution with zero expectation.

Usage

estimateSigmaMV(y,maxIter=100,epsilon=0.000001,verbose=FALSE)

Arguments

y

data matrix

maxIter

maximum number of iterations

epsilon

convergence criteria

verbose

print computation info or not

Value

Sigma

Estimated covariance matrix for y

m

Estimated shape parameter for inverse-gamma prior for gene variances

v

Estimated scale parameter for inverse-gamma prior for gene variances

converged

T if the EM algorithms converged

iter

Number of iterations

modS2

Moderated estimator of gene-specific variances

histLogS2

Histogram of log(s2) where s2 is the ordinary variance estimator

fittedDensityLogS2

The fitted density for log(s2)

Details

The multivariate t-distribution is parametrized as: $$y|c \sim N(\mu,c\Sigma)$$ $$c \sim \mbox{InvGamma}(m/2,m\nu/2)$$ Here $N$ denotes a multivariate normal distribution, $Sigma$ is a covariance matrix and $InvGamma(a,b)$ is the inverse-gamma distribution with density function $$f(x)=(\beta)^{\alpha} \exp\{-\beta/x\} x^{-\alpha-1}/\Gamma(\alpha)$$ In this application $mu$ equals zero, and m is the degrees of freedom.

References

Hastie, T., Tibshirani, R., and Friedman, J. (2001). The Elements of Statistical Learning, volume 1. Springer, first edition.

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

$A$strand, M. et al. (2007a). Improved covariance matrix estimators for weighted analysis of microarray data. Journal of Computational Biology, Accepted.

$A$strand, M. et al. (2007b). Empirical Bayes models for multiple-probe type arrays at the probe level. Bioinformatics, Submitted 1 October 2007.

See Also

estimateSigma