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This package provides a general framework for analyzing rank and preference data based on the Bayesian Mallows model.


To install the current release, use


To install the current development version, use

# install.packages("remotes")

Basic Usage Example

To get started, load the package with

The package comes with several example datasets. The simplest one contains 12 persons’ assessments of the weights of 20 potatoes, either by visual inspection (potato_visual) or by lifting the potatoes and comparing their relative weights by hand (potato_weighing).

Metropolis-Hastings Algorithm

To fit a Bayesian Mallows model on the potato_visual dataset using the Metropolis-Hastings algorithm first described in Vitelli et al. (2018), we do

potato_data <- setup_rank_data(potato_visual)
fit <- compute_mallows(data = potato_data)

Next, we can see a diagnostic plot for the Metropolis-Hastings algorithm with assess_convergence(). The plot below is for the scale parameter, which measures the variation between the individual rankings.

Setting the burnin to 500, we obtain a plot of the posterior distribution of the scale parameter with:

fit$burnin <- 500

For more examples, please see our the introductory vignette, and the function documentation. The use of parallel chains are described in this vignette.

Sequential Monte Carlo Algorithm

The package also supports updating a Bayesian Mallows model using sequential Monte Carlo, with the algorithm described in Stein (2023). For example, in order to update the model fitted above with the potato ranks based on comparing their relative weights by hand, we do

new_data <- setup_rank_data(rankings = potato_weighing)
updated_fit <- update_mallows(model = fit, new_data = new_data)

We can go on to plot the posterior distribution of the scale parameter for this updated model.


Sequential Monte Carlo can typically be useful when new data arrives in batches, as it does not require the Metropolis-Hastings algorithm to be rerun. See this vignette for more information.

The Bayesian Mallows Model


The BayesMallows package currently implements the complete model described in Vitelli et al. (2018), which includes a large number of distance metrics, handling of missing ranks and pairwise comparisons, and clustering of users with similar preferences. The extension to non-transitive pairwise comparisons by Crispino et al. (2019) is also implemented. In addition, the partition function of the Mallows model can be estimated using the importance sampling algorithm of Vitelli et al. (2018) and the asymptotic approximation of Mukherjee (2016). For a review of ranking models in general, see Liu, Crispino, et al. (2019). Crispino and Antoniano-Villalobos (2022) outlines how informative priors can be used within the model.

Updating of the posterior distribution based on new data, using sequential Monte Carlo methods, is implemented and described in a separate vignette. The computational algorithms are described in further detail in Stein (2023).


Among the current applications, Liu, Reiner, et al. (2019) applied the Bayesian Mallows model for providing personalized recommendations based on clicking data, and Barrett and Crispino (2018) used the model of Crispino et al. (2019) to analyze listeners’ understanding of music. Eliseussen, Fleischer, and Vitelli (2022) presented an extended model for variable selection in genome-wide transcriptomic analyses.

Future Extensions

Plans for future extensions of the package include implementation of a variational Bayes algorithm for approximation the posterior distribution. The sequential Monte Carlo algorithms will also be extended to cover a larger part of the model framework, and we will add more options for specifications of prior distributions.


If using the BayesMallows package in academic work, please cite Sørensen et al. (2020), in addition to the relevant methodological papers.

#> To cite package 'BayesMallows' in publications use:
#>   Sørensen Ø, Crispino M, Liu Q, Vitelli V (2020). "BayesMallows: An R
#>   Package for the Bayesian Mallows Model." _The R Journal_, *12*(1),
#>   324-342. doi:10.32614/RJ-2020-026
#>   <>.
#> A BibTeX entry for LaTeX users is
#>   @Article{,
#>     author = {{\O}ystein S{\o}rensen and Marta Crispino and Qinghua Liu and Valeria Vitelli},
#>     doi = {10.32614/RJ-2020-026},
#>     title = {BayesMallows: An R Package for the Bayesian Mallows Model},
#>     journal = {The R Journal},
#>     number = {1},
#>     pages = {324--342},
#>     volume = {12},
#>     year = {2020},
#>   }


This is an open source project, and all contributions are welcome. Feel free to open an Issue, a Pull Request, or to e-mail us.


Barrett, N., and Marta Crispino. 2018. “The Impact of 3-d Sound Spatialisation on Listeners’ Understanding of Human Agency in Acousmatic Music.” Journal of New Music Research 47 (5): 399–415.
Crispino, Marta, and Isadora Antoniano-Villalobos. 2022. “Informative Priors for the Consensus Ranking in the Bayesian Mallows Model.” Bayesian Analysis, January, 1–24.
Crispino, Marta, E. Arjas, V. Vitelli, N. Barrett, and A. Frigessi. 2019. “A Bayesian Mallows Approach to Nontransitive Pair Comparison Data: How Human Are Sounds?” The Annals of Applied Statistics 13 (1): 492–519.
Eliseussen, Emilie, Thomas Fleischer, and Valeria Vitelli. 2022. “Rank-Based Bayesian Variable Selection for Genome-Wide Transcriptomic Analyses.” Statistics in Medicine 41 (23): 4532–53.
Liu, Q., Marta Crispino, I. Scheel, V. Vitelli, and A. Frigessi. 2019. “Model-Based Learning from Preference Data.” Annual Review of Statistics and Its Application 6 (1).
Liu, Q., A. H. Reiner, A. Frigessi, and I. Scheel. 2019. “Diverse Personalized Recommendations with Uncertainty from Implicit Preference Data with the Bayesian Mallows Model.” Knowledge-Based Systems 186 (December): 104960.
Mukherjee, S. 2016. “Estimation in Exponential Families on Permutations.” The Annals of Statistics 44 (2): 853–75.
Sørensen, Øystein, Marta Crispino, Qinghua Liu, and Valeria Vitelli. 2020. “BayesMallows: An R Package for the Bayesian Mallows Model.” The R Journal 12 (1): 324–42.
Stein, Anja. 2023. “Sequential Inference with the Mallows Model.” PhD thesis, Lancaster University.
Vitelli, V., Ø. Sørensen, M. Crispino, E. Arjas, and A. Frigessi. 2018. “Probabilistic Preference Learning with the Mallows Rank Model.” Journal of Machine Learning Research 18 (1): 1–49.