estimateMVbeta {plw}R Documentation

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

Description

Estimate the parameters m and v of the multivariate t-distribution with zero expectation, where v is modeled as smooth function of a covariate. The covariance matrix Sigma is assumed to be known.

Usage

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

Arguments

y Data matrix
x Covariate vector
Sigma Covariance matrix
maxIter Maximum number of iterations
epsilon Convergence criterion
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 (2001). In this application mu equals zero, and m is the degrees of freedom.

Value

Sigma The input 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 TRUE 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, estimateSigmaMVbeta


[Package plw version 1.2.0 Index]