volleyball          package:hyperdirichlet          R Documentation

_R_e_s_u_l_t_s _f_r_o_m _t_h_e _N_O_C_S _v_o_l_l_e_y_b_a_l_l _l_e_a_g_u_e

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

     Results from the NOCS volleyball league.  Object
     'volleyball_results' is a matrix in which each column corresponds
     to a player and each row corresponds to a volleyball set; 'vb' is
     the corresponding likelihood function in the form of a
     hyperdirichlet distribution.

     Object 'vb_synthetic' is a hyperdirichlet object corresponding to
     a synthetic dataset obtained from 4000 simulated volleyball sets.

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

     data(volleyball)

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

     A volleyball set is a Bernoulli trial between two disjoint subsets
     of the players.  The two subsets are denoted (after the game) as
     the winners and the losers: these are denoted by '1' and '0'
     respectively.

     Thus the first line reads of 'volleyball_results' reads:


      p1  p2  p3  p4  p5  p6  p7  p8  p9 
      1    0  NA   1   0   0  NA   1  NA

     showing that the teams were 'p1', 'p4' and 'p8' against 'p2', 'p5'
     and 'p6'; players 'p3', 'p7' and 'p9' did not play.

     Dataset 'vb_synthetic' is the likelihood function of 4000
     simulated trials in which the skills are distributed according to
     Zipf's law: '1/(1:9)/sum(1/(1:9))'.

     These datasets illustrate the fact that such Bernoulli trials are
     only weakly informative.  The synthetic dataset involves 4000
     observations because this was about the minimum number for which
     one could estimate the probabilities reasonably reliably.  Even
     then, the lowest probabilities are poorly identified.

_S_o_u_r_c_e:

     Volleyball games at NOCS, 2006-2008

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

     data(volleyball)
     maximum_likelihood(vb , start_p = c(0.407, 0.091, 0.432, 1.73e-05,
     2.24e-08, 1.9e-05, 1.8e-07, 0.03, 0.039) , control=list(maxit=100))

     zipf <- 1/seq_len(9)
     maximum_likelihood(vb_synthetic , start_p=zipf, control=list(maxit=100))

