metropolis_hastings_aug_ranking

Function to perform Metropolis-Hastings for new augmented ranking

An implementation of the Bayesian version of the Mallows rank model
(Vitelli et al., Journal of Machine Learning Research, 2018 <https://jmlr.org/papers/v18/15-481.html>;
Crispino et al., Annals of Applied Statistics, 2019 <doi:10.1214/18-AOAS1203>;
Sorensen et al., R Journal, 2020 <doi:10.32614/RJ-2020-026>;
Stein, PhD Thesis, 2023 <https://eprints.lancs.ac.uk/id/eprint/195759>). Both Metropolis-Hastings
and sequential Monte Carlo algorithms for estimating the models are available. Cayley, footrule,
Hamming, Kendall, Spearman, and Ulam distances are supported in the models. The rank data to be
analyzed can be in the form of complete rankings, top-k rankings, partially missing rankings, as well
as consistent and inconsistent pairwise preferences. Several functions for plotting and studying the
posterior distributions of parameters are provided. The package also provides functions for estimating
the partition function (normalizing constant) of the Mallows rank model, both with the importance
sampling algorithm of Vitelli et al. and asymptotic approximation with the IPFP algorithm
(Mukherjee, Annals of Statistics, 2016 <doi:10.1214/15-AOS1389>).

Oystein Sorensen

BayesMallows

Bayesian Preference Learning with the Mallows Rank Model

Waldir Leoncio

Valeria Vitelli

Marta Crispino

Qinghua Liu

Cristina Mollica

Luca Tardella

Anja Stein

metropolis_hastings_aug_ranking function

<dl><dt>alpha</dt>
<dd>Numeric value of the scale parameter</dd>
<dt>rho</dt>
<dd>Numeric vector specifying the consensus ranking</dd>
<dt>n_items</dt>
<dd>Integer is the number of items in a ranking</dd>
<dt>partial_ranking</dt>
<dd>An incomplete rank sequence vector of the original observed incomplete ranking which contains NAs</dd>
<dt>current_ranking</dt>
<dd>An complete rank sequence vector of the proposed augmented ranking obtained from calculate_forward_probability function</dd>
<dt>pseudo</dt>
<dd>Boolean specifying whether to use pseudo proposal or not.s</dd>
<dt>metric</dt>
<dd>A character string specifying the distance metric to use in the
Bayesian Mallows Model. Available options are <code>"footrule"</code>,
<code>"spearman"</code>, <code>"cayley"</code>, <code>"hamming"</code>, <code>"kendall"</code>, and
<code>"ulam"</code>.</dd></dl>

Arguments

Metropolis-Hastings Augmented Ranking — metropolis_hastings_aug_ranking

<dl>

<dt>alpha</dt>
<dd>Numeric value of the scale parameter</dd>


<dt>rho</dt>
<dd>Numeric vector specifying the consensus ranking</dd>


<dt>n_items</dt>
<dd>Integer is the number of items in a ranking</dd>


<dt>partial_ranking</dt>
<dd>An incomplete rank sequence vector of the original observed incomplete ranking which contains NAs</dd>


<dt>current_ranking</dt>
<dd>An complete rank sequence vector of the proposed augmented ranking obtained from calculate_forward_probability function</dd>


<dt>pseudo</dt>
<dd>Boolean specifying whether to use pseudo proposal or not.s</dd>


<dt>metric</dt>
<dd>A character string specifying the distance metric to use in the
Bayesian Mallows Model. Available options are <code>"footrule"</code>,
<code>"spearman"</code>, <code>"cayley"</code>, <code>"hamming"</code>, <code>"kendall"</code>, and
<code>"ulam"</code>.</dd>

</dl>

metropolis_hastings_aug_ranking: Metropolis-Hastings Augmented Ranking

Description

Usage

Value

Arguments