estimateMVbeta              package:plw              R Documentation

_Z_e_r_o _m_e_a_n _m_u_l_t_i_v_a_r_i_a_t_e _t-_d_i_s_t. _w_i_t_h _c_o_v_a_r_i_a_t_e _d_e_p_e_n_d_e_n_t _s_c_a_l_e.

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

       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

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

   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

_A_u_t_h_o_r(_s):

     Magnus Astrand

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

     plw, lmw, estimateSigmaMVbeta

