arXiv subjects

Javier Enrique Aguilar

Publications and source records attributed to Javier Enrique Aguilar.

10 recordsLinked to original sources

arXiv2026

R2-GP: Variance-Calibrated Priors for Additive Gaussian Processes

We develop R2-GP, an R2D2-type prior for Gaussian process (GP) generalised additive models (GAMs) that calibrates explained variance ($R^2$) for Matérn covariance kernels. The function variance for standard Matérn kernels depends jointly on the effect magnitude and length-scale. As such, smooth and rough components with identical amplitudes contribute very different amounts of variation. With independent priors on component amplitudes, this variation results in variance overestimation, especially in higher dimensions. We overcome this by taking direct control over each component's expected contribution to prior explained variance. We do this by rescaling each component based on its length scale and observed inputs, and modelling each rescaled variance as a share of the function variance induced by a global $R^2$ prior. This allows R2-GP to scale well to many components. To also scale to large sample sizes, we extend R2-GP to Hilbert space approximation methods, a framework for kernels exploiting their spectral decompositions for fast and efficient inference. Our simulations and real-world case studies demonstrate superior generalisation and parameter recovery over independent variance priors.

stat.ML↗

arXiv2026

Dirichlet-Tree Allocation Priors for Bayesian Causal Forests

Bayesian Causal Forests (BCF) estimate heterogeneous treatment effects with a separate ensemble of treatment trees. The prior on the leaf values of the treatment trees determines whether sampling variability is attributed to the treatment effect. Independent shrinkage priors exert no control over how a tree allocates variability across its leaves, and their total prior variance grows as leaves are added. We propose the Dirichlet-Tree Bayesian Causal Forest, which jointly regularizes the leaf values of each treatment tree through a Dirichlet-Tree prior on their variance shares, generated by stick-breaking along the tree topology. We characterize the spike and tails of the marginal leaf prior, show that the prior adaptively bounds the number of regions of effect heterogeneity, and establish posterior consistency for the forest. In simulations, the model outperforms BCF when heterogeneity is confined to a few regions and reduces spurious heterogeneity elsewhere, and, unlike independent shrinkage priors, its accuracy does not deteriorate as the trees grow. We also evaluate the model on real data, including a pancreatic cancer survival study.

stat.ME↗

arXiv2025

Latent variable estimation with composite Hilbert space Gaussian processes

We develop a scalable class of models for latent variable estimation using composite Gaussian processes, with a focus on derivative Gaussian processes. We jointly model multiple data sources as outputs to improve the accuracy of latent variable inference under a single probabilistic framework. Similarly specified exact Gaussian processes scale poorly with large datasets. To overcome this, we extend the recently developed Hilbert space approximation methods for Gaussian processes to obtain a reduced-rank representation of the composite covariance function through its spectral decomposition. Specifically, we derive and analyze the spectral decomposition of derivative covariance functions and further study their properties theoretically. Using these spectral decompositions, our methods easily scale up to data scenarios involving thousands of samples. We validate our methods in terms of latent variable estimation accuracy, uncertainty calibration, and inference speed across diverse simulation scenarios. Finally, using a real world case study from single-cell biology, we demonstrate the potential of our models in estimating latent cellular ordering given gene expression levels, thus enhancing our understanding of the underlying biological process.

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arXiv2025

R2 priors for Grouped Variance Decomposition in High-dimensional Regression

We introduce the Group-R2 decomposition prior, a hierarchical shrinkage prior that extends R2-based priors to structured regression settings with known groups of predictors. By decomposing the prior distribution of the coefficient of determination R2 in two stages, first across groups, then within groups, the prior enables interpretable control over model complexity and sparsity. We derive theoretical properties of the prior, including marginal distributions of coefficients, tail behavior, and connections to effective model complexity. Through simulation studies, we evaluate the conditions under which grouping improves predictive performance and parameter recovery compared to priors that do not account for groups. Our results provide practical guidance for prior specification and highlight both the strengths and limitations of incorporating grouping into R2-based shrinkage priors.

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arXiv2025

Primed Priors for Simulation-Based Validation of Bayesian Models

Simulation-based calibration (SBC) is a method for validating inference algorithms and model implementations through repeated inference on data simulated from a generative model. For a model to be generative, one must specify proper priors. However, in all but the simplest of cases, choosing priors for every model parameter is a nontrivial task. In particular, priors that are too broad can produce numerical issues due to extreme parameter values while overly narrow ones can exclude precisely those regions of the parameter space where legitimate problems in the implementation would have manifested. When the data to be analyzed is already available, the issue can be sidestepped by checking calibration on the corresponding posterior, but that is not always a viable option. In this paper, we adapt the framework of catalytic priors, which have been recently proposed for construction of data-based prior distributions, and propose primed priors, which do not require real data and can therefore facilitate prior specification in SBC. We discuss relevant connections of primed priors to the theory of catalytic priors and show their use for SBC in three simulation studies.

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arXiv2025

Dependency-Aware Shrinkage Priors for High Dimensional Regression

In high dimensional regression, global local shrinkage priors have gained significant traction for their ability to yield sparse estimates, improve parameter recovery, and support accurate predictive modeling. While recent work has explored increasingly flexible shrinkage prior structures, the role of explicitly modeling dependencies among coefficients remains largely unexplored. In this paper, we investigate whether incorporating such structures into traditional shrinkage priors improves their performance. We introduce dependency-aware shrinkage priors, an extension of continuous shrinkage priors that integrates correlation structures inspired by Zellner's g prior approach. We provide theoretical insights into how dependence alters the prior and posterior structure, and evaluate the method empirically through simulations and real data. We find that modeling dependence can improve parameter recovery when predictors are strongly correlated, but offers only modest gains in predictive accuracy. These findings suggest that prior dependence should be used selectively and guided by the specific inferential goals of the analysis.

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arXiv2025

Generalized Decomposition Priors on R2

The adoption of continuous shrinkage priors in high-dimensional linear models has gained widespread attention due to their practical and theoretical advantages. Among them, the R2D2 prior has gained popularity for its intuitive specification of the proportion of explained variance (R2) and its theoretically grounded properties. The R2D2 prior allocates variance among regression terms through a Dirichlet decomposition. However, this approach inherently limits the dependency structure among variance components to the negative dependence modeled by the Dirichlet distribution, which is fully determined by the mean. This limitation hinders the prior's ability to capture more nuanced or positive dependency patterns that may arise in real-world data. To address this, we propose the Generalized Decomposition R2 (GDR2) prior, which replaces the Dirichlet decomposition with the more flexible Logistic-Normal distribution and its variants. By allowing richer dependency structures, the GDR2 prior accommodates more realistic and adaptable competition among variance components, enhancing the expressiveness and applicability of R2-based priors in practice. Through simulations and real-world benchmarks, we demonstrate that the GDR2 prior improves out-of-sample predictive performance and parameter recovery compared to the R2D2 prior. Our framework bridges the gap between flexibility in variance decomposition and practical implementation, advancing the utility of shrinkage priors in complex regression settings.

stat.ME↗

arXiv2025

Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference

Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to predictions, inference, and subsequent decision-relevant quantities. However, quantifying and then propagating the uncertainty of surrogates is usually limited to special analytic cases or is otherwise computationally very expensive. In this paper, we propose a framework enabling a scalable, Bayesian approach to surrogate modeling with thorough uncertainty quantification, propagation, and validation. Specifically, we present three methods for Bayesian inference with surrogate models given measurement data. This is a task where the propagation of surrogate uncertainty is especially relevant, because failing to account for it may lead to biased and/or overconfident estimates of the parameters of interest. We showcase our approach in three detailed case studies for linear and nonlinear real-world modeling scenarios. Uncertainty propagation in surrogate models enables more reliable and safe approximation of expensive simulators and will therefore be useful in various fields of applications.

stat.ML↗

arXiv2024

Glucodensity Functional Profiles Outperform Traditional Continuous Glucose Monitoring Metrics

Continuous glucose monitoring (CGM) data has revolutionized the management of type 1 diabetes, particularly when integrated with insulin pumps to mitigate clinical events such as hypoglycemia. Recently, there has been growing interest in utilizing CGM devices in clinical studies involving healthy and diabetes populations. However, efficiently exploiting the high temporal resolution of CGM profiles remains a significant challenge. Numerous indices -- such as time-in-range metrics and glucose variability measures -- have been proposed, but evidence suggests these metrics overlook critical aspects of glucose dynamic homeostasis. As an alternative method, this paper explores the clinical value of glucodensity metrics in capturing glucose dynamics -- specifically the speed and acceleration of CGM time series -- as new biomarkers for predicting long-term glucose outcomes. Our results demonstrate significant information gains, exceeding 20\% in terms of adjusted $R^2$, in forecasting glycosylated hemoglobin (HbA1c) and fasting plasma glucose (FPG) at five and eight years from baseline AEGIS data, compared to traditional non-CGM and CGM glucose biomarkers. These findings underscore the importance of incorporating more complex CGM functional metrics, such as the glucodensity approach, to fully capture continuous glucose fluctuations across different time-scale resolutions.

stat.AP↗

arXiv2023

Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior

The training of high-dimensional regression models on comparably sparse data is an important yet complicated topic, especially when there are many more model parameters than observations in the data. From a Bayesian perspective, inference in such cases can be achieved with the help of shrinkage prior distributions, at least for generalized linear models. However, real-world data usually possess multilevel structures, such as repeated measurements or natural groupings of individuals, which existing shrinkage priors are not built to deal with. We generalize and extend one of these priors, the R2D2 prior by Zhang et al. (2020), to linear multilevel models leading to what we call the R2D2M2 prior. The proposed prior enables both local and global shrinkage of the model parameters. It comes with interpretable hyperparameters, which we show to be intrinsically related to vital properties of the prior, such as rates of concentration around the origin, tail behavior, and amount of shrinkage the prior exerts. We offer guidelines on how to select the prior's hyperparameters by deriving shrinkage factors and measuring the effective number of non-zero model coefficients. Hence, the user can readily evaluate and interpret the amount of shrinkage implied by a specific choice of hyperparameters. Finally, we perform extensive experiments on simulated and real data, showing that our inference procedure for the prior is well calibrated, has desirable global and local regularization properties and enables the reliable and interpretable estimation of much more complex Bayesian multilevel models than was previously possible.

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