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

In plw: Probe level Locally moderated Weighted t-tests.

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

Details

The multivariate t-distribution is parametrized as:

y|c ~ N(mu,c*Sigma)

c ~ InvGamma(m/2,m*v/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)

v(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), Astrand et al. (2007a,2007b).

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

Author(s)

Magnus Astrand

References

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

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

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

Astrand, 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

plw documentation built on April 28, 2020, 6:38 p.m.