postmed             package:EbayesThresh             R Documentation

_P_o_s_t_e_r_i_o_r _m_e_d_i_a_n _e_s_t_i_m_a_t_o_r

_D_e_s_c_r_i_p_t_i_o_n:

     Given a data value or a vector of data, find the corresponding
     posterior median estimate(s) of the underlying signal value(s)

_U_s_a_g_e:

     postmed(x, w, prior = "laplace", a = 0.5)

_A_r_g_u_m_e_n_t_s:

       x: a data value or a vector of data

       w: the value of the prior probability that the signal is nonzero 

   prior: family of the nonzero part of the prior; can be "cauchy" or 
          "laplace" 

       a: the scale parameter of the nonzero part of the prior if the
          Laplace prior is used

_D_e_t_a_i_l_s:

     The routine calls the relevant one of the routines
     'postmed.laplace' or 'postmed.cauchy'. In the Laplace case, the
     posterior median is found explicitly, without any need for the
     numerical solution of an equation. In the quasi-Cauchy case, the
     posterior median is found by finding the zero, component by
     component, of the vector function 'cauchy.medzero'.

_V_a_l_u_e:

     If x is a scalar, the posterior median med(theta|x) where theta 
     is the mean of the distribution from which x is drawn.     If x is
     a vector with elements x_1, ... , x_n, then the vector returned
     has elements  med(theta_i|x_i), where each x_i has mean theta_i, 
     all with the given prior.

_N_o_t_e:

     If the quasicauchy prior is used, the argument 'a' is ignored. The
     routine calls the approprate one of 'postmed.laplace' or
     'postmed.cauchy'.

_A_u_t_h_o_r(_s):

     Bernard Silverman

_R_e_f_e_r_e_n_c_e_s:

     See 'ebayesthresh' and <URL: http://www.bernardsilverman.com>

_S_e_e _A_l_s_o:

     'postmean'

_E_x_a_m_p_l_e_s:

     postmed(c(-2,1,0,-4,8,50), w=0.05, prior="cauchy")
     postmed(c(-2,1,0,-4,8,50), w=0.2, prior="laplace", a=0.3)

