Eleni Dilma | Searcharxiv

arXiv2025

Hybrid Bayesian Models for Community Detection with Application to a Colombian Conflict Network

We introduce a flexible Bayesian framework for clustering nodes in undirected binary networks, motivated by the need to uncover structural patterns in complex environments. Building on the stochastic block model, we develop two hybrid extensions: the Class-Distance Model, which governs interaction probabilities through Euclidean distances between cluster-level latent positions, and the Class-Bilinear Model, which captures more complex relational patterns via bilinear interactions. We apply this framework to a novel network derived from the Colombian armed conflict, where municipalities are connected through the co-presence of armed actors, violence, and illicit economies. The resulting clusters align with empirical patterns of territorial control and trafficking corridors, highlighting the models' capacity to recover and explain complex dynamics. Full Bayesian inference is carried out via MCMC under both finite and nonparametric clustering priors. While the main application centers on the Colombian conflict, we also assess model performance using synthetic data as well as other two benchmark datasets.

stat.ME↗

arXiv2024

Bridged Posterior: Optimization, Profile Likelihood and a New Approach to Generalized Bayes

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss function to form a posterior density. Nevertheless, Gibbs posteriors are supported in high-dimensional spaces, and do not inherit the computational efficiency or constraint formulations from optimization. In this article, we explore a new generalized Bayes approach, viewing the likelihood as a function of data, parameters, and latent variables conditionally determined by an optimization sub-problem. Marginally, the latent variable given the data remains stochastic, and is characterized by its posterior distribution. This framework, coined bridged posterior, conforms to the Bayesian paradigm. Besides providing a novel generative model, we obtain a positively surprising theoretical finding that under mild conditions, the $\sqrt{n}$-adjusted posterior distribution of the parameters under our model converges to the same normal distribution as that of the canonical integrated posterior. Therefore, our result formally dispels a long-held belief that partial optimization of latent variables may lead to underestimation of parameter uncertainty. We demonstrate the practical advantages of our approach under several settings, including maximum-margin classification, latent normal models, and harmonization of multiple networks.

stat.ME↗