arXiv subjects

Santiago Marin

Publications and source records attributed to Santiago Marin.

4 recordsLinked to original sources

arXiv2026

Bayesian nonparametric modeling of dynamic pollution clusters through an autoregressive logistic-beta Stirling-gamma process

Fine suspended particulates (FSP), commonly known as PM2.5, are among the most harmful air pollutants, posing serious risks to population health and environmental integrity. As such, accurately identifying clusters of air-quality monitoring stations exhibiting similar FSP levels is essential for guiding targeted interventions and localized public-health response measures. This task, however, is notably nontrivial as FSP levels may depend on various regional and temporal factors, which should be incorporated in the modeling process. Thus, we capitalize on Bayesian nonparametric dynamic clustering ideas, in which clustering structures may be influenced by complex dependencies. Existing implementations of dynamic clustering, however, rely on copula-based dependent Dirichlet processes (DPs), presenting considerable computational challenges for real-world deployment. With this in mind, we propose a more efficient alternative for dynamic clustering by incorporating the novel ideas of logistic-beta dependent DPs. We also adopt a Stirling-gamma prior--a novel distribution family--on the concentration parameter of our underlying DP, easing the process of incorporating prior knowledge into the model. Efficient computational strategies for posterior inference are also presented. We apply our proposed method to identify dynamic clusters of air-quality monitoring stations across Chile and demonstrate its superior performance over existing approaches.

stat.ME↗

arXiv2025

Invariant fractocohesive length in thermally aged elastomers

The fractocohesive length - the ratio between fracture toughness and work-to-fracture - provides a material-specific length scale that characterizes the size-dependent fracture behavior of pristine elastomers. However, its relevance to thermally aged materials, where both toughness and work of fracture degrade dramatically, remains unexplored. Here, we demonstrate that despite severe thermal embrittlement, the fractocohesive length remains invariant throughout thermal aging, independent of temperature or duration. We verify this invariance experimentally for two elastomer systems (Styrene Butadiene Rubber and Silicone Rubber) at multiple aging temperatures for aging times up to eight weeks. This finding bridges a critical gap in fracture mechanics of aged polymers: while the evolution of work-to-fracture can be predicted from well-established constitutive models that track network changes (crosslink density and chain scission), the evolution of fracture toughness has lacked predictive frameworks. The invariance of fractocohesive length enables direct calculation of fracture toughness at any aging state from the predicted work of fracture, eliminating the need for extensive fracture testing on aged elastomers and providing a crucial missing link for computational fracture predictions in aged elastomeric components.

cond-mat.soft↗

arXiv2024

Adaptive Shrinkage with a Nonparametric Bayesian Lasso

Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping relatively intact the important ones. With this task in mind, we develop the nonparametric Bayesian Lasso, an adaptive and flexible shrinkage prior for Bayesian regression and variable selection, particularly useful when the number of predictors is comparable or larger than the number of available data points. We build on spike-and-slab Lasso ideas and extend them by placing a Dirichlet Process prior on the shrinkage parameters. The result is a prior on the regression coefficients that can be seen as an infinite mixture of Double Exponential densities, all offering different amounts of regularization, ensuring a more adaptive and flexible shrinkage. We also develop an efficient Markov chain Monte Carlo algorithm for posterior inference. Through various simulation exercises and real-world data analyses, we demonstrate that our proposed method leads to a better recovery of the true regression coefficients, a better variable selection, and better out-of-sample predictions, highlighting the benefits of the nonparametric Bayesian Lasso over existing shrinkage priors.

stat.ME↗

arXiv2024

BOB: Bayesian Optimized Bootstrap for Uncertainty Quantification in Gaussian Mixture Models

A natural way to quantify uncertainties in Gaussian mixture models (GMMs) is through Bayesian methods. That said, sampling from the joint posterior distribution of GMMs via standard Markov chain Monte Carlo (MCMC) imposes several computational challenges, which have prevented a broader full Bayesian implementation of these models. A growing body of literature has introduced the Weighted Likelihood Bootstrap and the Weighted Bayesian Bootstrap as alternatives to MCMC sampling. The core idea of these methods is to repeatedly compute maximum a posteriori (MAP) estimates on many randomly weighted posterior densities. These MAP estimates then can be treated as approximate posterior draws. Nonetheless, a central question remains unanswered: How to select the random weights under arbitrary sample sizes. We, therefore, introduce the Bayesian Optimized Bootstrap (BOB), a computational method to automatically select these random weights by minimizing, through Bayesian Optimization, a black-box and noisy version of the reverse Kullback-Leibler (KL) divergence between the Bayesian posterior and an approximate posterior obtained via random weighting. Our proposed method outperforms competing approaches in recovering the Bayesian posterior, it provides a better uncertainty quantification, and it retains key asymptotic properties from existing methods. BOB's performance is demonstrated through extensive simulations, along with real-world data analyses.

stat.ME↗