calculate_forward_probability

Function to calculate probability of assigning a set of
 specific ranks to an specific item
given its rank in the consensus ranking

internal

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

calculate_forward_probability function

<dl><dt>item_ordering</dt>
<dd>A vector of integer values to represent the specified
queue of which unranked item to assign a rank for the proposed augmented
ranking</dd>
<dt>partial_ranking</dt>
<dd>An incomplete rank sequence vector of the original
observed incomplete ranking which contains NAs</dd>
<dt>remaining_set</dt>
<dd>A vector of integer values to represent the elements
(ranks) missing from original observed ranking</dd>
<dt>rho</dt>
<dd>Numeric vector specifying the consensus ranking</dd>
<dt>alpha</dt>
<dd>Numeric value of the scale parameter</dd>
<dt>n_items</dt>
<dd>Integer is the number of items in a ranking</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

Calculate Forward Probability — calculate_forward_probability

<dl>

<dt>item_ordering</dt>
<dd>A vector of integer values to represent the specified
queue of which unranked item to assign a rank for the proposed augmented
ranking</dd>


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


<dt>remaining_set</dt>
<dd>A vector of integer values to represent the elements
(ranks) missing from original observed ranking</dd>


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


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


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

Calculate Forward Probability

calculate_forward_probability: Calculate Forward Probability

Description

Usage

Value

Arguments