arXiv subjects

Juan Sosa

Publications and source records attributed to Juan Sosa.

At least 37 records · Page 2Linked to original sources

arXiv2025

Advances in Bayesian Modeling: Applications and Methods

This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as hierarchical modeling, spatial modeling, higher-order Markov chains, and Bayesian nonparametrics, the study emphasizes practical implementations across diverse fields, including oceanography, climatology, epidemiology, astronomy, and financial analysis. The aim is to bridge theoretical underpinnings with real-world applications, illustrating the formulation of Bayesian models, elicitation of priors, computational strategies, and posterior and predictive analyses. By leveraging different computational methods, this paper provides insights into model fitting, goodness-of-fit evaluation, and predictive accuracy, addressing computational efficiency and methodological challenges across various datasets and domains.

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arXiv2024

An unified approach to link prediction in collaboration networks

This article investigates and compares three approaches to link prediction in colaboration networks, namely, an ERGM (Exponential Random Graph Model; Robins et al. 2007), a GCN (Graph Convolutional Network; Kipf and Welling 2017), and a Word2Vec+MLP model (Word2Vec model combined with a multilayer neural network; Mikolov et al. 2013a and Goodfellow et al. 2016). The ERGM, grounded in statistical methods, is employed to capture general structural patterns within the network, while the GCN and Word2Vec+MLP models leverage deep learning techniques to learn adaptive structural representations of nodes and their relationships. The predictive performance of the models is assessed through extensive simulation exercises using cross-validation, with metrics based on the receiver operating characteristic curve. The results clearly show the superiority of machine learning approaches in link prediction, particularly in large networks, where traditional models such as ERGM exhibit limitations in scalability and the ability to capture inherent complexities. These findings highlight the potential benefits of integrating statistical modeling techniques with deep learning methods to analyze complex networks, providing a more robust and effective framework for future research in this field.

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arXiv2024

Analysis of Bipartite Networks in Anime Series: Textual Analysis, Topic Clustering, and Modeling

This article analyzes a specific bipartite network that shows the relationships between users and anime, examining how the descriptions of anime influence the formation of user communities. In particular, we introduce a new variable that quantifies the frequency with which words from a description appear in specific word clusters. These clusters are generated from a bigram analysis derived from all descriptions in the database. This approach fully characterizes the dynamics of these communities and shows how textual content affect the cohesion and structure of the social network among anime enthusiasts. Our findings suggest that there may be significant implications for the design of recommendation systems and the enhancement of user experience on anime platforms.

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arXiv2024

Stochastic Gradient Variational Bayes in the Stochastic Blockmodel

Stochastic variational Bayes algorithms have become very popular in the machine learning literature, particularly in the context of nonparametric Bayesian inference. These algorithms replace the true but intractable posterior distribution with the best (in the sense of Kullback-Leibler divergence) member of a tractable family of distributions, using stochastic gradient algorithms to perform the optimization step. stochastic variational Bayes inference implicitly trades off computational speed for accuracy, but the loss of accuracy is highly model (and even dataset) specific. In this paper we carry out an empirical evaluation of this trade off in the context of stochastic blockmodels, which are a widely used class of probabilistic models for network and relational data. Our experiments indicate that, in the context of stochastic blockmodels, relatively large subsamples are required for these algorithms to find accurate approximations of the posterior, and that even then the quality of the approximations provided by stochastic gradient variational algorithms can be highly variable.

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arXiv2024

Identifying Hierarchical Structures in Network Data

In this paper, we introduce a hierarchical extension of the stochastic blockmodel to identify multilevel community structures in networks. We also present a Markov chain Monte Carlo (MCMC) and a variational Bayes algorithm to fit the model and obtain approximate posterior inference. Through simulated and real datasets, we demonstrate that the model successfully identifies communities and supercommunities when they exist in the data. Additionally, we observe that the model returns a single supercommunity when there is no evidence of multilevel community structure. As expected in the case of the single-level stochastic blockmodel, we observe that the MCMC algorithm consistently outperforms its variational Bayes counterpart. Therefore, we recommend using MCMC whenever the network size allows for computational feasibility.

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arXiv2024

A robust Bayesian latent position approach for community detection in networks with continuous attributes

The increasing prevalence of multiplex networks has spurred a critical need to take into account potential dependencies across different layers, especially when the goal is community detection, which is a fundamental learning task in network analysis. We propose a full Bayesian mixture model for community detection in both single-layer and multi-layer networks. A key feature of our model is the joint modeling of the nodal attributes that often come with the network data as a spatial process over the latent space. In addition, our model for multi-layer networks allows layers to have different strengths of dependency in the unique latent position structure and assumes that the probability of a relation between two actors (in a layer) depends on the distances between their latent positions (multiplied by a layer-specific factor) and the difference between their nodal attributes. Under our prior specifications, the actors' positions in the latent space arise from a finite mixture of Gaussian distributions, each corresponding to a cluster. Simulated examples show that our model outperforms existing benchmark models and exhibits significantly greater robustness when handling datasets with missing values. The model is also applied to a real-world three-layer network of employees in a law firm.

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arXiv2024

International Trade Network: Statistical Analysis and Modeling

Globalization has rapidly advanced but exposed countries to supply chain disruptions, highlighted by the COVID-19 pandemic. This study exhaustively analyzes bilateral export data for 186 countries from 2018, 2020, and 2022, using Exponential Random Graph Models (ERGMs), to identify determinants of trade relationships, as well as Stochastic Block Models (SBMs), to characterize countries' roles in the trade network. Our findings show persistent, significant nodal characteristics driving bilateral trade and reveal no major structural changes in the trade network due to the pandemic.

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arXiv2024

Leadership and Engagement Dynamics in Legislative Twitter Networks: Statistical Analysis and Modeling

In this manuscript, we analyze the interaction network on Twitter among members of the 117th U.S. Congress to assess the visibility of political leaders and explore how systemic properties and node attributes influence the formation of legislative connections. We employ descriptive social network statistical methods, the exponential random graph model (ERGM), and the stochastic block model (SBM) to evaluate the relative impact of network systemic properties, as well as institutional and personal traits, on the generation of online relationships among legislators. Our findings reveal that legislative networks on social media platforms like Twitter tend to reinforce the leadership of dominant political actors rather than diminishing their influence. However, we identify that these leadership roles can manifest in various forms. Additionally, we highlight that online connections within legislative networks are influenced by both the systemic properties of the network and institutional characteristics.

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arXiv2024

Semiparametric Modelling of Cancer Mortality Trends in Colombia

In this paper, we compare semiparametric and parametric model adjustments for cancer mortality in breast and cervical cancer and prostate and lung cancer in men, according to age and period of death. Semiparametric models were adjusted for the number of deaths from the two localizations of greatest mortality by sex: breast and cervix in women; prostate and lungs in men. Adjustments in different semiparametric models were compared; which included making adjustments with different distributions and variable combinations in the parametric and non-parametric part, for localization as well as for scale. Finally, the semiparametric model with best adjustment was selected and compared to traditional model; that is, to the generalized lineal model with Poisson response and logarithmic link. Best results for the four kinds of cancer were obtained for the selected semiparametric model by comparing it to the traditional Poisson model based upon AIC, envelope correlation between estimated logarithm rate and real rate logarithm. In general, we observe that in estimation, rate increases with age; however, with respect to period, breast cancer and stomach cancer in men show a tendency to rise over time; on the other hand, for cervical cancer, it remains virtually constant, but for lung cancer in men, as of 2007, it tends to decrease.

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arXiv2024

Bayesian Cointegrated Panels in Digital Marketing

In this paper, we fully develop and apply a novel extension of Bayesian cointegrated panels modeling in digital marketing, particularly in modeling of a system where key ROI metrics such as clicks or impressions of a given digital campaign considered. Thus, in this context our goal is evaluating how the system reacts to investment perturbations due to changes in the investment strategy and its impact on the visibility of specific campaigns. To do so, we fit the model using a set of real marketing data with different investment campaigns over the same geographic territory. By employing forecast error variance decomposition, our findings indicate that clicks and impressions have a significant impact on session generation. Also, we evaluate our approach through a comprehensive simulation study that considers different processes. The results indicate that our proposal has substantial capabilities in terms of estimability and accuracy.

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arXiv2024

Influence Networks: Bayesian Modeling and Diffusion

In this article, we make an innovative adaptation of a Bayesian latent space model based on projections in a novel way to analyze influence networks. By appropriately reparameterizing the model, we establish a formal metric for quantifying each individual's influencing capacity and estimating their latent position embedded in a social space. This modeling approach introduces a novel mechanism for fully characterizing the diffusion of an idea based on the estimated latent characteristics. It assumes that each individual takes the following states: Unknown, undecided, supporting, or rejecting an idea. This approach is demonstrated using a influence network from Twitter (now $\mathbb{X}$) related to the 2022 Tax Reform in Colombia. An exhaustive simulation exercise is also performed to evaluate the proposed diffusion process.

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arXiv2023

Characterization of the presidential inauguration speech and identification of political communities in Colombia: An empirical approach from the analysis of social networks

Statistical analysis of social networks is a predominant methodology in political science research. In this article we implement network methods to characterize the presidential inauguration speech and identify political communities in Colombia. We propose an empirical approach to analize the discursive structure of the heads of state and the configuration of alliance and work relationships between prominent figures of Colombian politics. Thus, we implement network methods from two perspectives, words and political actors. We conclude on the relevance of social network statistics to identify frequent and important terms in the communicative action of president figures, and to examine cohesion such discourses. Finally, we distinguish notable actors in the consolidation of working relationships and alliances as well as political communities.

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arXiv2023

Bayesian Analysis for Social Science Research

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for a broad audience, not necessarily with specialized knowledge in Bayesian statistics, yet having interest in incorporating this kind of methods in studying social phenomena. We illustrate Bayesian methods through case studies regarding political surveys, population dynamics, and standardized educational testing. Specifically, we provide technical details on specific topics such as conjugate and non-conjugate modeling, hierarchical modeling, Bayesian computation, goodness of fit, and model testing.

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arXiv2023

Conditional Relative Risk: An association measure for longitudinal data analysis

In this paper, we propose a novel association measure for longitudinal studies based on the traditional definition of relative risk. In a Markovian fashion, such a proposal takes into account the information content regarding the previous time. We derive its corresponding confidence interval by means of the Delta method having in mind the crude association between factor and event. Also, we study the properties of our uncertainty quantification scheme through an exhaustive simulation study. Our findings show that the coverage probability is quite close to the level of confidence. Finally, our proposal has a reasonable interpretation from the epidemiological as well as the statistical point of view.

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arXiv2022

Bayesian modeling of the political preferences of the Colombian Senate 2006-2010: electoral behavior and parapolitics

In this paper, a Bayesian spatial voting model is applied for the first time to characterize the legislative behavior of the Senate of the Republic of Colombia for the period 2006-2010. The analysis is carried out based on the plenary nominal votes of the Senate. The estimation of the model is done using Markov Monte Carlo chain algorithms. The estimated ideal points provide empirical evidence supporting a latent non-ideological feature (opposition--non-opposition) underlying senators' voting. Additionally, the relationship between the parapolitics scandal and the legislative behavior of senators is analyzed through a logistic model, both Bayesian and frequentist. The results indicate a significant relationship between being or having been involved with the parapolitics scandal and the legislative behavior of the senators from the period 2006-2010.

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arXiv2022

Operationalizing Legislative Bodies: A Methodological and Empirical Perspective

This manuscript extensively reviews applications, extensions, and models derived from the Bayesian ideal point estimator. We primarily focus our attention on studies conducted in the United States as well as Latin America. First, we provide a detailed description of the Bayesian ideal point estimator. Next, we propose a new taxonomy to synthesize and frame technical developments and applications associated with the estimator in the context of North American and Latin American governing bodies. The literature available in Latin America allows us to conclude that few legislatures in the region have been analyzed using the methodology under discussion. Also, we highlight those parliaments of Latin America embedded in democratic presidential systems as novel scenarios for operationalizing the electoral behavior of legislative bodies through nominal voting data. Our findings show some alternatives for future research. Finally, to fix ideas and illustrate the capabilities of the Bayesian ideal point estimator, we present an application involving the Colombian House of Representatives 2010-2014.

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arXiv2022

Small area estimation using multiple imputation in three-parameter logistic models

We propose a novel methodology relating item response theory methods with small area estimation strategies in the presence of missing data. Specifically, we propose an unbiased estimator for the average ability parameter of three-parameter logistic models. Thus, we carry out an extensive simulation study in order to compare our estimator with the well-known Horvitz-Thompson estimator. According to our experiments with synthetic data, our proposal has substantial lower standard errors than its competitor. In addition, we perform an actual application by considering the Mathematics results of the 2015 Program for International Student Assessment (PISA), and also, compare our results with previous analyses. Our findings strongly suggest that our methodology is a high competitive alternative for generating compelling official statistics.

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arXiv2021

Some Case Studies Using Bayesian Statistical Models

We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks, such as description, testing, estimation, and prediction. This work is not meant to be either a reference text or a survey in Bayesian statistical inference. Our goal is simply to provide several examples that use Bayesian methodology to solve data-driven problems. The topics we cover here, include problems in Bayesian nonparametrics, Bayesian analysis of times series, and Bayesian analysis of spatial data.

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