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 1.0.0 Index]