Performs a probabilistic rank analysis based on an almost uniform sample of possible rankings that preserve a partial ranking.

mcmc_rank_prob(P, rp = nrow(P)^3)

P | P A partial ranking as matrix object calculated with neighborhood_inclusion or positional_dominance. |
---|---|

rp | Integer indicating the number of samples to be drawn. |

Estimated expected ranks of nodes

Matrix containing estimated relative rank probabilities:
`relative.rank[u,v]`

is the probability that u is ranked lower than v.

This function can be used instead of exact_rank_prob
if the number of elements in `P`

is too large for an exact computation. As a rule of thumb,
the number of samples should be at least cubic in the number of elements in `P`

.
See `vignette("benchmarks",package="netrankr")`

for guidelines and benchmark results.

Bubley, R. and Dyer, M., 1999. Faster random generation of linear extensions.
*Discrete Mathematics*, **201**(1):81-88

if (FALSE) { data("florentine_m") P <- neighborhood_inclusion(florentine_m) res <- exact_rank_prob(P) mcmc <- mcmc_rank_prob(P,rp = vcount(g)^3) # mean absolute error (expected ranks) mean(abs(res$expected.rank-mcmc$expected.rank)) }