randomprobs {aylmer}R Documentation

Probabilities of random boards

Description

Probabilities of a random Markov chain of boards, chosen by the Metropolis-Hastings algorithm

Usage

randomprobs(x, B=2000, n=100, burnin = 0,  use.brob=FALSE, func=NULL)
candidate(x, n = 100, give = FALSE)

Arguments

x Matrix, coerced to class board: the start point
B Number of samples to take
burnin Number of samples to discard at the beginning
use.brob Boolean, with default FALSE meaning to use IEEE arithmetic and TRUE meaning to use Brobdingnagian arithmetic
n The number of times to try to find a candidate board with no non-negative entries; special value 0 means to search until one is found
func In function randomprobs(), the statistic to return; default of NULL interpreted as prob()
give In function candidate(), Boolean with default FALSE meaning to return a permissible board, and TRUE meaning to return instead the number of attempts made to find a permissible board (zero meaning no board was found). See details section below

Value

Returns a vector of length B with entries corresponding to the probabilities of the boards encountered

Note

Argument n of function candidate() specifies how many times to search for a board with no non-negative entries. The special value n=0 means to search until one is found.

Boards with a large number of zeros may require more than the default 100 attempts to find a permissible board. Set the give flag to see how many candidates are generated before a permissible one is found.

Warning: a board with at most one entry greater than zero is the unique permissible board and the algorithm will not terminate if n=0

A board that requires more than 100 attempts is probably well-suited to the exact test as permissible boards will likely be enumerable using allboards().

Author(s)

Robin K. S. Hankin (R); Luke J. West (C++)

References

See Also

aylmer.test

Examples

data(chess)
aylmer.test(chess)

a <- matrix(1,9,9)
plot(randomprobs(a,1000),type="b",main="Importance of burn-in")

set.seed(0)
b <- diag(rep(6,6))
plot(randomprobs(b,B=1000,n=1000), type="b",main="Importance of burn-in, part II")


[Package aylmer version 1.0-3 Index]