Description Usage Details Source References Examples
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.
1 |
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:
1 2 |
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.
Volleyball games at NOCS, 2006-2008
Robin K. S. Hankin (2010). “A Generalization of the Dirichlet Distribution”, Journal of Statistical Software, 33(11), 1-18, http://www.jstatsoft.org/v33/i11/
1 2 3 4 5 6 7 | 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))
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