arXiv subjects

Jonas Arruda

Publications and source records attributed to Jonas Arruda.

7 recordsLinked to original sources

arXiv2026

Hierarchical Bayesian inference with compositional score modeling for stellar streams

Context: Stellar streams trace the gravitational potential of the Milky Way over a wide range of Galactocentric radii. Since different streams sample different regions of the Galaxy, combining several of them can constrain the global mass distribution more tightly than modeling any single stream in isolation. Most of the existing multi-stream analyses rely on likelihood-based methods that require a new inference run whenever additional streams or kinematic measurements become available. Aims: We aim to infer the Milky Way potential from multiple stellar streams combined with an additional constraint through the Galactic circular velocity curve within a single hierarchical framework. Methods: We model the problem hierarchically, separating parameters that are common to all streams from parameters that are specific to each progenitor. We train score-based neural posterior estimators on a library of simulated streams and combine information from different streams through compositional score modeling as a post-training step. Results: Tests on independent simulations show that the inferred posteriors are well calibrated and accurate. Combining several streams reduces the uncertainties on the global potential parameters relative to single-stream analyses. Applied to Gaia data, the model favours a mildly oblate dark matter halo with axis ratio $q_{NFW} = 0.77$, scale radius $a_{NFW} = 9.3$ kpc, a disk mass of $4.3 \times 10^{10} M_\odot$, and a local dark matter density $\rho_{NFW,\odot} = 0.01153 M_\odot pc^{-3}$ consistent with recent stream-based studies. Conclusions: This hierarchical framework provides a practical way to combine information from multiple stellar streams without repeating the full inference procedure for each new dataset. The method is adaptable to new datasets, like future Gaia DR4, or new spectroscopic surveys, with minimal computational cost.

astro-ph.GA↗

arXiv2026

NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia

Nonlinear mixed-effects models are widely used to analyze longitudinal data, but existing open-source software often supports only a limited subset of the model structures, inference methods, machine-learning components, automatic differentiation techniques, and random-effects distributions required in modern applications. We introduce NoLimits.jl, an open-source Julia package for flexible and composable nonlinear mixed-effects modeling. Its macro-based modeling language enables observation and latent-state models to be constructed from diverse building blocks, including ordinary differential equations, Markov models, and neural networks. NoLimits.jl supports flexible, covariate-dependent observation and random-effects distributions and provides a unified interface to frequentist inference through Laplace approximation, stochastic expectation maximization, and Bayesian Markov chain Monte Carlo methods. We demonstrate the package on three case studies showcasing its workflows, integration of differentiable machine-learning components, and data-driven estimation of random-effects distributions using normalizing flows. Together, these capabilities substantially expand the range of nonlinear mixed-effects models that can be specified, estimated, and compared within a single open-source framework.

stat.CO↗

arXiv2026

Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in epidemiological or survey settings, individuals with certain outcomes may be more likely to be included, resulting in biased prevalence estimates with potentially substantial downstream impact. Classical corrections, such as inverse-probability weighting or explicit likelihood-based models of the selection process, rely on tractable likelihoods, which limits their applicability in complex stochastic models with latent dynamics or high-dimensional structure. Simulation-based inference enables Bayesian analysis without tractable likelihoods but typically assumes missingness at random and thus fails when selection depends on unobserved outcomes or covariates. Here, we develop a bias-aware simulation-based inference framework that explicitly incorporates selection into neural posterior estimation. By embedding the selection mechanism directly into the generative simulator, the approach enables amortized Bayesian inference without requiring tractable likelihoods. This recasting of selection bias as part of the simulation process allows us to both obtain debiased estimates and explicitly test for the presence of bias. The framework integrates diagnostics to detect discrepancies between simulated and observed data and to assess posterior calibration. The method recovers well-calibrated posterior distributions across three statistical applications with diverse selection mechanisms, including settings in which likelihood-based approaches yield biased estimates. These results recast the correction of selection bias as a simulation problem and establish simulation-based inference as a practical and testable strategy for parameter estimation under selection bias.

stat.ML↗

arXiv2026

MEmilio -- A high performance Modular EpideMIcs simuLatIOn software for multi-scale and comparative simulations of infectious disease dynamics

Epidemic and pandemic preparedness with rapid outbreak response rely on timely, trustworthy evidence. Mathematical models are crucial for supporting timely and reliable evidence generation for public health decision-making with models spanning approaches from compartmental and metapopulation models to detailed agent-based simulations. Yet, the accompanying software ecosystem remains fragmented across model types, spatial resolutions, and computational targets, making models harder to compare, extend, and deploy at scale. Here we present MEmilio, a modular, high-performance framework for epidemic simulation that harmonizes the specification and execution of diverse dynamic epidemiological models within a unified and harmonized architecture. MEmilio couples an efficient C++ simulation core with coherent model descriptions and a user-friendly Python interface, enabling workflows that run on laptops as well as high-performance computing systems. Standardized representations of space, demography, and mobility support straightforward adaptations in resolution and population size, facilitating systematic inter-model comparisons and ensemble studies. The framework integrates readily with established tools for uncertainty quantification and parameter inference, supporting a broad range of applications from scenario exploration to calibration. Finally, strict software-engineering practices, including extensive unit and continuous integration testing, promote robustness and minimize the risk of errors as the framework evolves. By unifying implementations across modeling paradigms, MEmilio aims to lower barriers to reuse and generalize models, enable principled comparisons of implicit assumptions, and accelerate the development of novel approaches that strengthen modeling-based outbreak preparedness.

q-bio.PE↗

arXiv2026

BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python

Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid inference of any model-implied quantity, such as point estimates, likelihoods, or full posterior distributions. In this work, we present the Python library BayesFlow, Version 2.0, for general-purpose ABI. Along with direct posterior, likelihood, and ratio estimation, the software includes support for multiple popular deep learning backends, a rich collection of generative networks for sampling and density estimation, complete customization and high-level interfaces, as well as new capabilities for hyperparameter optimization, design optimization, and hierarchical modeling. Using a case study on dynamical system parameter estimation, combined with comparisons to similar software, we show that our streamlined, user-friendly workflow has strong potential to support broad adoption.

stat.CO↗

arXiv2025

Diffusion Models in Simulation-Based Inference: A Tutorial Review

Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.

stat.ML↗

arXiv2025

Compositional amortized inference for large-scale hierarchical Bayesian models

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, has been a major hurdle due to the need to simulate and process massive datasets. Our study tackles these challenges by extending compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. We develop a new error-damping estimator to address previous stability issues of CSM when aggregating large numbers of data points. We first verified the numerical stability with up to 100,000 data points on a controlled benchmark. We then evaluated our method on a hierarchical AR model, achieving competitive performance to direct ABI baselines on smaller problem sizes while using less than one full model simulation for larger problem sizes. Finally, we address a large-scale inverse problem in advanced microscopy with over 750,000 parameters, demonstrating its relevance to real scientific applications.

q-bio.QM↗