randomprobs: 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)
randomboards(x, B=2000, n=100, burnin=0)
candidate(x, n = 100, give = FALSE)

Arguments

Matrix, coerced to class board: the start point

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

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

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

References

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

Examples

Run this code

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)