Performs a probabilistic rank analysis based on an almost uniform sample of possible rankings that preserve a partial ranking.
Usage
mcmc_rank_prob(P, rp = nrow(P)^3)Arguments
- 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.
Value
- expected.rank
Estimated expected ranks of nodes
- relative.rank
Matrix containing estimated relative rank probabilities:
relative.rank[u,v]is the probability that u is ranked lower than v.
Details
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.
References
Bubley, R. and Dyer, M., 1999. Faster random generation of linear extensions. Discrete Mathematics, 201(1):81-88
Examples
if (FALSE) { # \dontrun{
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))
} # }