postmean            package:EbayesThresh            R Documentation

_P_o_s_t_e_r_i_o_r _m_e_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 mean estimate(s) of the underlying signal value(s)

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

     postmean(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

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

     If x is a scalar, the posterior mean E(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 E(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. If
     'prior="laplace"', the routine calls 'postmean.laplace', which
     finds the posterior mean explicitly, as the product of the
     posterior probability that the parameter is nonzero and the
     posterior mean conditional on not being zero.    If
     'prior="cauchy"', the routine calls 'postmean.cauchy'; in that
     case the posterior mean is found by expressing the quasi-Cauchy
     prior as a mixture: The mean conditional on the mixing parameter
     is found and is then averaged  over the posterior distribution of
     the mixing parameter,  including the atom of probability at zero
     variance.

_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:

     'postmed'

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

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

