Bayesian Plackett--Luce latent block models for ranked data

We introduce a Bayesian latent block model that jointly partitions assessors and items under a Plackett--Luce observation model.

Assessors are assigned to $C$ clusters and items to $K$ blocks; items in a block share a common strength parameter within each assessor cluster, yielding a parsimonious $C\times K$ co-clustering representation.

Independent Gnedin priors infer $C$ and $K$.

Data augmentation gives conjugate Gibbs updates and a tractable MCMC sampler with split-merge moves.

Simulations characterize recovery and posterior uncertainty as signal, ranking depth, and group balance vary.

Applied to the cancer gene atlas (TCGA) pan-cancer top-500 gene-expression rankings, the model reveals tissue-driven sample structure while compressing gene-level heterogeneity into interpretable blocks.

Rank-based GSEA of posterior gene scores supports biological interpretation.