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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. Spatial factor modeling: A Bayesian matrix‐normal approach for misaligned data

   https://doi.org/10.1111/biom.13452  

   Zhang, Lu; Banerjee, Sudipto (March 2021, Biometrics)

   Abstract Multivariate spatially oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for each variable and associations among the different dependent variables. Multivariate latent spatial process models have proved effective in driving statistical inference and rendering better predictive inference at arbitrary locations for the spatial process. High‐dimensional multivariate spatial data, which are the theme of this article, refer to data sets where the number of spatial locations and the number of spatially dependent variables is very large. The field has witnessed substantial developments in scalable models for univariate spatial processes, but such methods for multivariate spatial processes, especially when the number of outcomes are moderately large, are limited in comparison. Here, we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesian inference, which is attractive for full uncertainty quantification of the latent spatial process. Our approach exploits distribution theory for the matrix‐normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high‐dimensional parameter space including the latent spatial process. We illustrate the computational and inferential benefits of our algorithms over competing methods using simulation studies and an analysis of a massive vegetation index data set. 

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3. High‐dimensional multivariate geostatistics: A Bayesian matrix‐normal approach

   https://doi.org/10.1002/env.2675  

   Zhang, Lu; Banerjee, Sudipto; Finley, Andrew_O (February 2021, Environmetrics)

   Abstract Joint modeling of spatially oriented dependent variables is commonplace in the environmental sciences, where scientists seek to estimate the relationships among a set of environmental outcomes accounting for dependence among these outcomes and the spatial dependence for each outcome. Such modeling is now sought for massive data sets with variables measured at a very large number of locations. Bayesian inference, while attractive for accommodating uncertainties through hierarchical structures, can become computationally onerous for modeling massive spatial data sets because of its reliance on iterative estimation algorithms. This article develops a conjugate Bayesian framework for analyzing multivariate spatial data using analytically tractable posterior distributions that obviate iterative algorithms. We discuss differences between modeling the multivariate response itself as a spatial process and that of modeling a latent process in a hierarchical model. We illustrate the computational and inferential benefits of these models using simulation studies and analysis of a vegetation index data set with spatially dependent observations numbering in the millions. 

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4. 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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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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