arXiv subjects

Spencer Wadsworth

Publications and source records attributed to Spencer Wadsworth.

6 recordsLinked to original sources

arXiv2026

Bayesian Sparsity Modeling of Shared Neural Response in Functional Magnetic Resonance Imaging Data

Detecting shared neural activity from functional magnetic resonance imaging (fMRI) across individuals exposed to the same stimulus can reveal synchronous brain responses, functional roles of regions, and potential clinical biomarkers. Intersubject correlation (ISC) is the main method for identifying voxelwise shared responses and per-subject variability, but it relies on heavy data summarization and thousands of regional tests, leading to poor uncertainty quantification and multiple testing issues. ISC also does not directly estimate a shared neural response (SNR) function. We propose a model-based alternative applicable to both task-based and naturalistic fMRI that simultaneously identifies spatial regions of shared activity and estimates the SNR function. The model combines sparse Gaussian process estimation of the response function with a Bayesian sparsity prior inspired by the horseshoe prior to detect voxel activation. A spatially structured extension encourages neighboring voxels to exhibit similar activation patterns. We examine the model's properties, evaluate performance via simulations, and analyze two real-world fMRI datasets, including one task-based and one naturalistic dataset. The Bayesian framework provides principled uncertainty quantification for the shared response function and shows improved activation detection and response estimation compared to standard approaches. Model fits demonstrate comparable or superior performance relative to ISC, while the framework opens avenues for clinical applications.

stat.AP↗

arXiv2025

Quantile Forecast Matching with a Bayesian Quantile Gaussian Process Model

A set of probabilities along with corresponding quantiles are often used to define predictive distributions or probabilistic forecasts. These quantile predictions offer easily interpreted uncertainty of an event, and quantiles are generally straightforward to estimate using standard statistical and machine learning methods. However, compared to a distribution defined by a probability density or cumulative distribution function, a set of quantiles has less distributional information. When given estimated quantiles, it may be desirable to estimate a fully defined continuous distribution function. Many researchers do so to make evaluation or ensemble modeling simpler. Most existing methods for fitting a distribution to quantiles lack accurate representation of the inherent uncertainty from quantile estimation or are limited in their applications. In this manuscript, we present a Gaussian process model, the quantile Gaussian process, which is based on established theory of quantile functions and sample quantiles, to construct a probability distribution given estimated quantiles. A Bayesian application of the quantile Gaussian process is evaluated for parameter inference and distribution approximation in simulation studies. The quantile Gaussian process is used to approximate the distributions of quantile forecasts from the 2023-24 US Centers for Disease Control collaborative flu forecasting initiative. The simulation studies and data analysis show that the quantile Gaussian process leads to accurate inference on model parameters, estimation of a continuous distribution, and uncertainty quantification of sample quantiles.

stat.ME↗

arXiv2025

Bayesian Stacking via Proper Scoring Rule Optimization using a Gibbs Posterior

In collaborative forecast projects, the combining of multiple probabilistic forecasts into an ensemble is standard practice, with linear pooling being a common combination method. The weighting scheme of a linear pool should be tailored to the specific research question, and weight selection is often performed via optimizing a proper scoring rule. This is known as optimal linear pooling. Besides optimal linear pooling, Bayesian predictive synthesis has emerged as a model probability updating scheme which is more flexible than standard Bayesian model averaging and which provides a Bayesian solution to selecting model weights for a linear pool. In many problems, equally weighted linear pool forecasts often outperform forecasts constructed using sophisticated weight selection methods. Thus regularization to an equal weighting of forecasts may be a valuable addition to any weight selection method. In this manuscript, we introduce an optimal linear pool based on a Gibbs posterior over stacked model weights optimized over a proper scoring rule. The Gibbs posterior extends stacking into a Bayesian framework by allowing for optimal weight solutions to be influenced by a prior distribution, and it also provides uncertainty quantification of weights in the form of a probability distribution. We compare ensemble forecast performance with model averaging methods and equal weighted models in simulation studies and in a real data example from the 2023-24 US Centers for Disease Control FluSight competition. In both the simulation studies and the FluSight analysis, the stacked Gibbs posterior produces ensemble forecasts which often outperform the ensembles of other methods.

stat.ME↗

arXiv2025

Forecasting Influenza Hospitalizations Using a Bayesian Hierarchical Nonlinear Model with Discrepancy

The annual influenza outbreak leads to significant public health and economic burdens making it desirable to have prompt and accurate probabilistic forecasts of the disease spread. The United States Centers for Disease Control and Prevention (CDC) hosts annually a national flu forecasting competition which has led to the development of a variety of flu forecast modeling methods. Beginning in 2013, the target to be forecast was weekly percentage of patients with an influenza-like illness (ILI), but in 2021 the target was changed to weekly hospitalizations. Reliable hospitalization data has only been available since 2021, but ILI data has been available since 2010 and has been successfully forecast for several seasons. In this manuscript, we introduce a two component modeling framework for forecasting hospitalizations utilizing both hospitalization and ILI data. The first component is for modeling ILI data using a nonlinear Bayesian model. The second component is for modeling hospitalizations as a function of ILI. For hospitalization forecasts, ILI is first forecast then hospitalizations are forecast with ILI forecasts used as a predictor. In a simulation study, the hospitalization forecast model is assessed and two previously successful ILI forecast models are compared. Also assessed is the usefulness of including a systematic model discrepancy term in the ILI model. Forecasts of state and national hospitalizations for the 2023-24 flu season are made, and different modeling decisions are compared. We found that including a discrepancy component in the ILI model tends to improve forecasts during certain weeks of the year. We also found that other modeling decisions such as the exact nonlinear function to be used in the ILI model or the error distribution for hospitalization models may or may not be better than other decisions, depending on the season, location, or week of the forecast.

stat.AP↗

arXiv2023

Mixture distributions for probabilistic forecasts of disease outbreaks

Collaboration among multiple teams has played a major role in probabilistic forecasting events of influenza outbreaks, the COVID-19 pandemic, other disease outbreaks, and in many other fields. When collecting forecasts from individual teams, ensuring that each team's model represents forecast uncertainty according to the same format allows for direct comparison of forecasts as well as methods of constructing multi-model ensemble forecasts. This paper outlines several common probabilistic forecast representation formats including parametric distributions, sample distributions, bin distributions, and quantiles and compares their use in the context of collaborative projects. We propose the use of a discrete mixture distribution format in collaborative forecasting in place of other formats. The flexibility in distribution shape, the ease for scoring and building ensemble models, and the reasonably low level of computer storage required to store such a forecast make the discrete mixture distribution an attractive alternative to the other representation formats.

stat.AP↗

arXiv2020

Role of surface defects and material inhomogeneities for vortex nucleation in superconductors within time-dependent Ginzburg-Landau theory in 2 and 3 dimensions

We use Time-Dependent Ginzburg-Landau theory to study the nucleation of vortices in type II superconductors in the presence of both geometric and material inhomogeneities. The superconducting Meissner state is meta-stable up to a critical magnetic field, known as the superheating field. For a uniform surface and homogenous material, the superheating transition is driven by a non-local critical mode in which an array of vortices simultaneously penetrate the surface. In contrast, we show that even a small amount of disorder localizes the critical mode and can have a significant reduction in the effective superheating field for a particular sample. Vortices can be nucleated by either surface roughness or local variations in material parameters, such as Tc. Our approach uses a finite element method to simulate a cylindrical geometry in 2 dimensions and a film geometry in 2 and 3 dimensions. We combine saddle node bifurcation analysis along with a novel fitting procedure to evaluate the superheating field and identify the unstable mode. We demonstrate agreement with previous results for homogenous geometries and surface roughness and extend the analysis to include variations in material properties. Finally, we show that in three dimensions, suface divots not aligned with the applied field can increase the super heating field. We discuss implications for fabrication and performance of superconducting resonant frequency cavities in particle accelerators.

physics.comp-ph↗