estimateSigmaMV             package:plw             R Documentation

_F_i_t _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_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     estimate the parameters Sigma, m and v of the multivariate
     t-distribution with zero expectation.

_U_s_a_g_e:

     estimateSigmaMV(y,maxIter=100,epsilon=0.000001,verbose=FALSE)

_A_r_g_u_m_e_n_t_s:

       y: data matrix

 maxIter: maximum number of iterations

 epsilon: convergence criteria

 verbose: print computation info or not

_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)

     Here 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)

     In this application mu equals zero, and m is the degrees of
     freedom.

_V_a_l_u_e:

   Sigma: Estimated covariance matrix for y

       m: Estimated shape parameter for inverse-gamma prior for gene
          variances

       v: Estimated scale parameter 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)

_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:

     estimateSigma

