arXiv subjects

Hisaya Okahara

Publications and source records attributed to Hisaya Okahara.

3 recordsLinked to original sources

arXiv2026

The Covariate-Assisted Bayesian Intransitive Bradley-Terry Model via Combinatorial Hodge Theory

Pairwise comparison data are widely used to recover latent rankings, yet the models in dominant use assume stochastic transitivity. When preferences are in fact intransitive, a single scalar strength conflates genuine hierarchy with cycle-induced structure, biasing both the recovered ranking and any covariate effects attributed to it. To address this limitation, we propose the Covariate-Assisted Bayesian Intransitive Bradley-Terry (CA-BIBT) model, which uses a combinatorial Hodge decomposition to resolve the latent match-up into identifiable and mutually orthogonal flows, attributing the component lying in the covariate-induced subspace to observed covariates and assigning the remaining components to the residuals. A global-local shrinkage prior on the residual cycle-induced flow adapts the model from transitive to intransitive regimes without prespecifying the regime, and a Gibbs sampler yields, as posterior byproducts, calibrated uncertainty for each flow, the posterior probability of the level at which the entities are rankable, and two complementary decision summaries that remain well-defined under intransitivity. In simulations, the CA-BIBT model recovers all flow components accurately with near-nominal coverage, and in applications to two animal dominance datasets, it distinguishes covariate-induced from residual cyclic dominance while quantifying posterior uncertainty, and demonstrates the practical utility of two complementary decision summaries.

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arXiv2025

Modeling asymmetry in multi-way contingency tables with ordinal categories via f-divergence

This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a rational model under the presence of a ``prior guess.'' Inspired by the constraints used in the derivation of multivariate normal distributions, we demonstrate that the proposed model minimizes f-divergence from complete symmetry under specific constraints. The proposed model encompasses existing asymmetry models as special cases while offering remarkably high interpretability. By modifying divergence measures included in f-divergence, the model provides the flexibility to adapt to specific probabilistic structures of interest. Furthermore, we established theorems that show that a complete symmetry model can be decomposed into two or more models, each imposing less restrictive parameter constraints. We also investigated the properties of the goodness-of-fit statistics with an emphasis on the likelihood ratio and Wald test statistics. Extensive Monte Carlo simulations confirmed the nominal size, high power, and robustness of the choice of f-divergence. Finally, an application to real-world data highlights the practical utility of the proposed model for analyzing asymmetric structures in ordinal contingency tables.

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arXiv2024

A generalized ordinal quasi-symmetry model and its separability for analyzing multi-way tables

This paper addresses the challenge of modeling multi-way contingency tables for matched set data with ordinal categories. Although the complete symmetry and marginal homogeneity models are well established, they may not always provide a satisfactory fit to the data. To address this issue, we propose a generalized ordinal quasi-symmetry model that offers increased flexibility when the complete symmetry model fails to capture the underlying structure. We investigate the properties of this new model and provide an information-theoretic interpretation, elucidating its relationship to the ordinal quasi-symmetry model. Moreover, we revisit Agresti's findings and present a new necessary and sufficient condition for the complete symmetry model, proving that the proposed model and the marginal moment equality model are separable hypotheses. We demonstrate the practical application of our model through empirical studies on medical and public opinion datasets. Comprehensive simulation studies evaluate the proposed model under various scenarios, including model's performance for multivariate normal data and asymptotic behavior. It enables researchers to examine the symmetry structure in the data with greater precision, providing a more thorough understanding of the underlying patterns. This powerful framework equips researchers with the necessary tools to explore the complexities of ordinal variable relationships in matched data sets, paving the way for new discoveries and insights.

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