plw (version 1.30.0)

estimateSigmaMVbeta: Zero mean multivariate t-dist. with covariate dependent scale.

Description

Estimate the parameters $Sigma$, $m$ and $v$ of the multivariate t-distribution with zero expectation, where $v$ is modeled as smooth function of a covariate.

Usage

estimateSigmaMVbeta(y, x, maxIter = 200, epsilon = 1e-06, verbose = FALSE, nknots = 10, nOut = 2000, nIn = 4000, iterInit = 3, br = NULL)

Arguments

y

Data matrix

x

Covariate vector

maxIter

Maximum number of iterations

epsilon

Convergence criteria

verbose

Print computation info or not

nknots

Number of knots of spline for $v$

nOut

Parameter for calculating knots, see getKnots

nIn

Parameter for calculating knots, see getKnots

iterInit

Number of iteration in when initiating $Sigma$

br

Knots, overrides nknots, n.out and n.in

Value

Sigma

Estimated covariance matrix for y

m

Estimated shape parameter for inverse-gamma prior for gene variances

v

Estimated scale parameter curve 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)

logs2

Variance estimators, logged with base 2.

beta

Estimated parameter vector $beta$ of spline for $v(x)$

knots

The knots used in spline for $v(x)$

x

The input vector covariate vector x

Details

The multivariate t-distribution is parametrized as: $$y|c \sim N(\mu,c\Sigma)$$ $$c \sim \mbox{InvGamma}(m/2,m\nu/2)$$ where $v$ is function of the covariate x: $v(x)$ and $N$ denotes a multivariate normal distribution, $Sigma$ is a covariance matrix and $InvGamma(a,b)$ is the inverse-gamma distribution with density function $$f(x)=(b)^{a} \exp\{-b/x\} x^{-a-1}/\Gamma(a)$$

A cubic spline is used to parameterize the smooth function $v(x)$ $$\nu(x) = \exp\{ H(x)^T \beta \}$$ where $H:R->R^(2p-1)$ is a set B-spline basis functions for a given set of p interior spline-knots, see chapter 5 of Hastie et al. (2001). In this application $mu$ equals zero, and m is the degrees of freedom.

For details about the model see Kristiansson et al. (2005), $A$strand et al. (2007a,2007b).

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

plw, lmw