randomprobs: Probabilities of random boards
In aylmer: A generalization of Fisher's exact test

Description Usage Arguments Value Note Author(s) References See Also Examples

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

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

`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

Function randomprobs() returns a vector of length B with entries corresponding to the probabilities of the boards encountered.

Function randomboards() returns an array with slices being successive boards

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().

To find the permissible board that maximizes some objective function, use best(), which applies the bespoke optimization routines of optim()

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

N. A. Metropolis and others 1953. Equation of State Calculations by Fast Computing Machines. Journal of Chemical Physics, 21:1087–1092

aylmer.test,best

data(chess)
aylmer.test(chess)

a <- matrix(1,9,9)    # See Sloane's A110058
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")


data(purum)
randomboards(purum,10)