arXiv subjects

Isaías Bañales

Publications and source records attributed to Isaías Bañales.

3 recordsLinked to original sources

arXiv2026

Understanding the Hamiltonian Monte Carlo through its Physics Fundamentals and Examples

The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how Hamiltonian dynamics work and why they can be used in a MCMC algorithm. This work elucidates the Monte Carlo Hamiltonian, providing comprehensive explanations of the underlying physical concepts. It is intended for readers with a solid foundation in mathematics who may lack familiarity with specific physical concepts, such as those related to Hamiltonian dynamics. Additionally, we provide Python code for the HMC algorithm, examples and comparisons with the Random Walk Metropolis-Hastings (RWMH) algorithm, alongside an exploration of modern variants such as the No-U-Turn Sampler (NUTS), the Dual Averaging (DA) scheme and the repelling-attracting HMC (raHMC), to highlight HMC's strengths and weaknesses when applied to Bayesian Inference.

stat.CO↗

arXiv2026

Estimating Inhomogeneous Spatio-Temporal Background Intensity Functions using Graphical Dirichlet Processes

An enhancement in seismic measuring instrumentation has been proven to have implications in the quantity of observed earthquakes, since denser networks usually allow recording more events. However, phenomena such as strong earthquakes or even aseismic transients, as slow slip earthquakes, may alter the occurrence of earthquakes. In the field of seismology, it is a standard practice to model background seismicity as a Poisson process. Based on this idea, this work proposes a model that can incorporate the evolving spatial intensity of Poisson processes over time (i.e., we include temporal changes in the background seismicity when modeling). In recent years, novel methodologies have been developed for quantifying the uncertainty in the estimation of the background seismicity in homogeneous cases using Bayesian non-parametric techniques. This work proposes a novel methodology based on graphical Dirichlet processes for incorporating spatial and temporal inhomogeneities in background seismicity. The proposed model in this work is applied to study the seismicity in the southern Mexico, using recorded data from 2000 to 2015.

stat.AP↗

arXiv2025

Branching Stein Variational Gradient Descent for sampling multimodal distributions

We propose a novel particle-based variational inference method designed to work with multimodal distributions. Our approach, referred to as Branched Stein Variational Gradient Descent (BSVGD), extends the classical Stein Variational Gradient Descent (SVGD) algorithm by incorporating a random branching mechanism that encourages the exploration of the state space. In this work, a theoretical guarantee for the convergence in distribution is presented, as well as numerical experiments to validate the suitability of our algorithm. Performance comparisons between the BSVGD and the SVGD are presented using the Wasserstein distance between samples and the corresponding computational times.

cs.LG↗