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

1 2 3 | ```
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 |

`B` |
Number of samples to take |

`burnin` |
Number of samples to discard at the beginning |

`use.brob` |
Boolean, with default |

`n` |
The number of times to try to
find a candidate board with no non-negative entries; special
value |

`func` |
In function |

`give` |
In function |

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

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
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)
``` |

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