# mcmc_rank_prob: Estimate rank probabilities with Markov Chains In netrankr: Analyzing Partial Rankings in Networks

 mcmc_rank_prob R Documentation

## Estimate rank probabilities with Markov Chains

### Description

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.

### 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.

### 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.

David Schoch

### References

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

exact_rank_prob, approx_rank_relative, approx_rank_expected

### 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)
``````

netrankr documentation built on Aug. 20, 2023, 5:06 p.m.