# randomprobs

0th

Percentile

##### Probabilities of random boards

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

Keywords
array
##### Usage
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)
##### 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

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

##### 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().

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

##### References

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

aylmer.test,best

• randomprobs
• randomboards
• candidate
##### Examples
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)


Documentation reproduced from package aylmer, version 1.0-11, License: GPL-2

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