Approximate Bayesian inference for cumulative probit regression models

Ordinal categorical data are routinely encountered in a wide range of practical applications. When the primary goal is to construct a regression model for ordinal outcomes, cumulative link models represent one of the most popular choices to link the cumulative probabilities of the response with a set of covariates through a parsimonious linear predictor, shared across response categories. When the number of observations grows, standard sampling algorithms for Bayesian inference scale poorly, making posterior computation increasingly challenging in large datasets. In this article, we propose three scalable algorithms for approximating the posterior distribution of the regression coefficients in cumulative probit models relying on Variational Bayes and Expectation Propagation. We compare the proposed approaches with inference based on Markov Chain Monte Carlo, demonstrating superior computational performance and remarkable accuracy; finally, we illustrate the utility of the proposed algorithms on a challenging case study to investigate the structure of a criminal network.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2511.06967
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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