hyperdirichlet (version 1.5-1)

volleyball: Results from the NOCS volleyball league

Description

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.

Usage

data(volleyball)

Details

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.

References

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/

Examples

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))