mcmc_rank_prob function

Estimate rank probabilities with Markov Chains

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)

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.

Returns

• 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.

Examples

## Not run:

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))
## End(Not run)

References

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

See Also

exact_rank_prob , approx_rank_relative , approx_rank_expected

Author(s)

David Schoch