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1. Variational Phylodynamic Inference Using Pandemic-scale Data

   https://doi.org/10.1093/molbev/msac154  

   Ki, Caleb; Terhorst, Jonathan (August 2022, Molecular Biology and Evolution)

   Rogers, Rebekah (Ed.)

   Abstract The ongoing global pandemic has sharply increased the amount of data available to researchers in epidemiology and public health. Unfortunately, few existing analysis tools are capable of exploiting all of the information contained in a pandemic-scale data set, resulting in missed opportunities for improved surveillance and contact tracing. In this paper, we develop the variational Bayesian skyline (VBSKY), a method for fitting Bayesian phylodynamic models to very large pathogen genetic data sets. By combining recent advances in phylodynamic modeling, scalable Bayesian inference and differentiable programming, along with a few tailored heuristics, VBSKY is capable of analyzing thousands of genomes in a few minutes, providing accurate estimates of epidemiologically relevant quantities such as the effective reproduction number and overall sampling effort through time. We illustrate the utility of our method by performing a rapid analysis of a large number of SARS-CoV-2 genomes, and demonstrate that the resulting estimates closely track those derived from alternative sources of public health data. 

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2. Demonstrating the Power and Flexibility of Variational Assumptions for Amortized Neural Posterior Estimation in Environmental Applications

   https://doi.org/10.1002/env.70074  

   Maceda, Elliot; Hector, Emily C; Lenzi, Amanda; Reich, Brian J (January 2026, Environmetrics)

   ABSTRACT Classic Bayesian methods with complex environmental models are frequently infeasible due to an intractable likelihood. Simulation‐based inference methods, such as neural posterior estimation, calculate posteriors without accessing a likelihood function by leveraging the fact that data can be quickly simulated from the model, but converge slowly and/or poorly in high‐dimensional settings. In this paper, we suggest that imposing strict variational assumptions on the form of the posterior can often combat these computational issues. Posterior distributions of model parameters are efficiently obtained by assuming a parametric form for the posterior, parametrized by the machine learning model, which is trained with the simulated data as inputs and the associated parameters as outputs. We show theoretically that if the parametric family of the variational posterior is correct, our posteriors converge to the true posteriors in Kullback–Leibler divergence. We also provide tools to help us identify if our parametric assumption is close to the true posterior, and modeling options if that is not the case. Comprehensive simulation studies using environmental models highlight our method's robustness and versatility. An analysis of the Zika virus in Brazil provides a thorough case study. 

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3. Easy Variational Inference for Categorical Models via an Independent Binary Approximation

   Michael T Wojnowicz, Shuchin Aeron (January 2022, The 39th International Conference on Machine Learning,)

   We pursue tractable Bayesian analysis of generalized linear models (GLMs) for categorical data. GLMs have been difficult to scale to more than a few dozen categories due to non-conjugacy or strong posterior dependencies when using conjugate auxiliary variable methods. We define a new class of GLMs for categorical data called categorical-from-binary (CB) models. Each CB model has a likelihood that is bounded by the product of binary likelihoods, suggesting a natural posterior approximation. This approximation makes inference straightforward and fast; using well-known auxiliary variables for probit or logistic regression, the product of binary models admits conjugate closed-form variational inference that is embarrassingly parallel across categories and invariant to category ordering. Moreover, an independent binary model simultaneously approximates multiple CB models. Bayesian model averaging over these can improve the quality of the approximation for any given dataset. We show that our approach scales to thousands of categories, outperforming posterior estimation competitors like Automatic Differentiation Variational Inference (ADVI) and No U-Turn Sampling (NUTS) in the time required to achieve fixed prediction quality. 

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4. Bayesian quantile regression with subset selection: A decision analysis perspective

   https://doi.org/10.1214/25-AOAS2053  

   Feldman, Joseph; Kowal, Daniel R (September 2025, The Annals of Applied Statistics)

   Quantile regression is a powerful tool in epidemiological studies where interest lies in inferring how different exposures affect specific percentiles of the distribution of a health or life outcome. Existing methods either estimate conditional quantiles separately for each quantile of interest or estimate the entire conditional distribution using semi- or nonparametric models. The former often produce inadequate models for real data and do not share information across quantiles, while the latter are characterized by complex and constrained models that can be difficult to interpret and computationally inefficient. Further, neither approach is well suited for quantile-specific subset selection. Instead, we pose the fundamental problems of linear quantile estimation, uncertainty quantification, and subset selection from a Bayesian decision analysis perspective. For any Bayesian regression model, we derive optimal and interpretable linear estimates and uncertainty quantification for each model-based conditional quantile. Our approach introduces a quantile-focused squared error loss, which enables efficient, closed-form computing and maintains a close relationship with Wasserstein-based density estimation. In an extensive simulation study, our methods demonstrate substantial gains in quantile estimation accuracy, variable selection, and inference over frequentist and Bayesian competitors. We use these tools to identify and quantify the heterogeneous impacts of multiple social stressors and environmental exposures on educational outcomes across the full spectrum of low- , medium- , and high-achieving students in North Carolina. 

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5. Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7Be System

   https://doi.org/10.3389/fphy.2022.888476  

   Odell, Daniel; Brune, Carl R.; Phillips, Daniel R.; deBoer, Richard James; Paneru, Som Nath (June 2022, Frontiers in Physics)

   Phenomenological R -matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist ( χ 2 -based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee , has been implemented for the R -matrix code AZURE2 , creating the Bayesian R -matrix Inference Code Kit ( BRICK ). Bayesian uncertainty estimation has then been carried out for a simultaneous R -matrix fit of the 3 He ( α , γ ) 7 Be and 3 He ( α , α ) 3 He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α -particle asymptotic normalization coefficients in 7 Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence. 

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