arXiv subjects

Paul F. V. Wiemann

Publications and source records attributed to Paul F. V. Wiemann.

9 recordsLinked to original sources

arXiv2026

Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields

Latent field models are essential for spatial statistics, but the posterior distribution of the latent field, even with a Gaussian process (GP) prior, is analytically intractable whenever the likelihood is non-Gaussian. Existing approximations are either too slow or too restrictive for large non-Gaussian datasets. We present a scalable variational inference framework that mirrors the sparse nearest-neighbor autoregressive structure of the prior in the variational family, uses normalizing-flow conditionals for expressiveness, and amortizes all variational parameters via a single shared neural conditioner. Doubly stochastic optimization with reduced ancestor sets achieves polylogarithmic complexity per iteration.

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arXiv2026

Generative multi-scale modeling via spatial autoregressive transport maps

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by fine-scale data (e.g., from regional climate models), which are typically computationally expensive to generate. Statistical downscaling and multi-scale data fusion address this challenge by predicting high-resolution fields from low-resolution or related inputs. We propose a highly scalable Bayesian approach that can learn the joint non-Gaussian distribution and nonlinear dependence structure of nonstationary spatial fields across multiple scales from a small number of training samples. Our method employs scale-aware autoregressive Gaussian processes with suitably chosen regularization-inducing priors to model the conditional distribution of fine-scale fields given coarse-scale data. Exploiting conjugacy, the integrated likelihood is available in closed form, enabling efficient parameter optimization via stochastic gradient descent. Once trained, the method provides a closed-form characterization of the posterior distribution of fine-scale fields given coarse-scale inputs. In numerical comparisons, we demonstrate that our approach substantially outperforms existing methods and effectively characterizes and simulates fine-scale climate behavior based on output from coarse global circulation models.

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arXiv2026

Data-Efficient Generative Modeling of Non-Gaussian Global Climate Fields via Scalable Composite Transformations

Quantifying uncertainty in climate-model output requires characterizing internal variability, often through large ensembles of physical climate-model runs. Since each additional ensemble member is computationally expensive, only limited numbers of replicated fields are typically available under a fixed model configuration and forcing scenario. We propose a data-efficient stochastic generator for the internal variability of global climate fields, specifically designed to overcome these sample-size constraints. The framework targets the distribution of climate-model output under fixed forcing and model physics. Inspired by copula modeling, our approach constructs a highly expressive joint distribution via a composite transformation to a multivariate standard normal space. We combine a nonparametric Bayesian transport map for spatial dependence modeling with flexible, spatially varying marginal models, essential for capturing non-Gaussian behavior and heavy-tailed extremes. These marginals are defined by a parametric model followed by a semi-parametric B-spline correction to capture complex distributional features. The marginal parameters are spatially smoothed using Gaussian-process priors with low-rank approximations, rendering the computational cost linear in the spatial dimension. When applied to global log-precipitation-rate fields under fixed forcing at more than 50,000 grid locations, our stochastic surrogate achieves high fidelity, accurately quantifying the climate distribution's spatial dependence and marginal characteristics, including the tails. Using only 10 training fields, it outperforms a state-of-the-art competitor trained on 80 fields, effectively octupling the computational budget for climate research. We provide a Python implementation at https://github.com/jobrachem/ppptm .

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arXiv2026

Bayesian Penalized Transformation Models: Structured Additive Location-Scale Regression for Arbitrary Conditional Distributions

Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive predictors. The core of the model is a monotonically increasing transformation function that relates the response distribution to a reference distribution. The transformation function is equipped with a smoothness prior that regularizes how much the estimated distribution diverges from the reference. PTMs can be seen as a bridge between conditional transformation models and generalized additive models for location, scale and shape. Markov chain Monte Carlo inference for PTMs offers straightforward uncertainty quantification for the conditional distribution as well as for the covariate effects. A simulation study demonstrates the effectiveness of the approach and includes comparisons to many alternative methods. Applications to the Fourth Dutch Growth Study and the Framingham Heart Study illustrate the usage and practical utility. A full-featured implementation is available as a Python library. Supplementary material for this article is available online.

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arXiv2026

Liesel: A Python Framework for Graph-Based Bayesian Modeling and Customizable MCMC with Support for Generalized Additive Models

Liesel is a Python framework for Bayesian model building and posterior computation with dedicated support for generalized additive regression models that is designed to reduce friction in methodological work. The framework consists of three components. The first component, Liesel-Model, represents models as directed acyclic graphs and supports interactive model construction, modification, visualization, prediction, and prior or posterior predictive simulation. The second component, Liesel-Goose, provides a modular MCMC framework based on reusable kernels and supports blocked componentwise sampling as well as user-defined Gibbs and Metropolis--Hastings updates, while leveraging JAX for automatic differentiation, just-in-time compilation, and hardware acceleration. The third component, Liesel-GAM, supplies high-level building blocks for generalized additive regression models and provides functionality for formula-based model specification, summaries, diagnostics, and effect visualization. Together, these parts make Liesel an effective tool for the rapid development, testing, and application of Bayesian models and MCMC algorithms. Liesel's modular architecture allows users to extend the software to models and inference algorithms beyond generalized additive models and MCMC, offering considerable flexibility for a wide spectrum of statistical research.

stat.CO↗

arXiv2026

Bayesian structured additive quantile regression for inflated bounded data

Bounded continuous data on the unit interval frequently arise in applied fields and often exhibit a non-negligible proportion of observations at the boundaries. Inflated regression models address this feature by combining a continuous distribution on the unit interval with a discrete component to account for zero- and/or one-inflation. In this paper, we propose a class of Bayesian structured additive quantile regression models for inflated bounded continuous data that accommodates zero- and/or one-inflation. The proposed approach enables direct modeling of both the conditional quantiles of the continuous component and the probabilities of observing zeros and/or ones, with structured additive predictors incorporated in both parts, including nonlinear effects, spatial effects, random effects, and varying-coefficient terms. Posterior inference is carried out using Markov chain Monte Carlo algorithms implemented through the software Liesel, a probabilistic programming framework for semiparametric regression. The practical performance of the proposed models is illustrated through simulation studies and two real-data applications: one analyzing the proportion of traffic-related fatalities across Brazilian municipal districts, and another evaluating speech intelligibility in cochlear implant recipients under different experimental conditions.

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arXiv2025

Bayesian spatial+: A joint model perspective

Spatial confounding is a common issue in spatial regression models, occurring when spatially varying covariates correlate with the spatial effect included in the model. This dependence, particularly at high spatial frequencies, can introduce bias in regression coefficient estimates when combined with smoothing penalties. The spatial+ framework is a widely used two-stage frequentist approach that mitigates spatial confounding by explicitly modeling and removing the spatial structure in the confounding covariate, then using the corresponding residuals in the second-stage model for the response. However, it does not propagate first-stage uncertainty, does not discuss a general inferential framework, and, crucially, cannot guarantee that covariate residuals and spatial effects in the response model are free of shared high-frequency structure, so confounding may persist. We propose Bayesian spatial+, a joint modeling approach that simultaneously addresses these limitations. Our framework naturally propagates uncertainty and enables straightforward posterior inference, while ensuring separation of spatial frequencies through specialized joint priors on smoothness parameters. We further introduce a cut-feedback strategy that prevents feedback between model components from reintroducing confounding. Simulation studies and real-world applications show substantial gains in bias reduction and interval coverage relative to existing approaches. Notably, in our comparisons, Bayesian spatial+ is the only method for which credible interval coverage remains stable as the sample size increases.

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arXiv2023

Bayesian nonparametric generative modeling of large multivariate non-Gaussian spatial fields

Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between the fields might also differ substantially. Extending a recently proposed Bayesian approach to describe the distribution of a nonstationary univariate spatial field using a triangular transport map, we cast the inference problem for a multivariate spatial field for a small number of replicates into a series of independent Gaussian process (GP) regression tasks with Gaussian errors. Due to the potential nonlinearity in the conditional means, the joint distribution modeled can be non-Gaussian. The resulting nonparametric Bayesian methodology scales well to high-dimensional spatial fields. It is especially useful when only a few training samples are available, because it employs regularization priors and quantifies uncertainty. Inference is conducted in an empirical Bayes setting by a highly scalable stochastic gradient approach. The implementation benefits from mini-batching and could be accelerated with parallel computing. We illustrate the extended transport-map model by studying hydrological variables from non-Gaussian climate-model output.

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arXiv2021

Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyond

Response functions linking regression predictors to properties of the response distribution are fundamental components in many statistical models. However, the choice of these functions is typically based on the domain of the modeled quantities and is not further scrutinized. For example, the exponential response function is usually assumed for parameters restricted to be positive although it implies a multiplicative model which may not necessarily be desired. Consequently, applied researchers might easily face misleading results when relying on defaults without further investigation. As an alternative to the exponential response function, we propose the use of the softplus function to construct alternative link functions for parameters restricted to be positive. As a major advantage, we can construct differentiable link functions corresponding closely to the identity function for positive values of the regression predictor, which implies an quasi-additive model and thus allows for an additive interpretation of the estimated effects by practitioners. We demonstrate the applicability of the softplus response function using both simulations and real data. In four applications featuring count data regression and Bayesian distributional regression, we contrast our approach to the commonly used exponential response function.

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