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1. On the mth-order Affine Pólya-Szegö Principle

   https://doi.org/10.1007/s12220-025-02039-8  

   Langharst, Dylan; Roysdon, Michael; Zhao, Yiming (May 2025, The Journal of Geometric Analysis)

   Abstract An affine Pólya-Szegö principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the$$L^p$$ $L^p$affine Pólya-Szegö principles due to Cianchi, Lutwak, Yang and Zhang, and subsequently Haberl, Schuster and Xiao. Various applications of this new Pólya-Szegö principle are shown. 

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2. PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits

   Dumitrascu, Bianca; Feng, Karen; Engelhardt, Barbara E. (January 2018, Neural Information Processing - Letters and Reviews)

   We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Pólya-Gamma distributed augmentation variables, we propose an improved version of Thompson Sampling, a Bayesian formulation of contextual bandits with near-optimal performance. Our approach, Pólya-Gamma augmented Thompson Sampling (PG-TS), achieves state-of-the-art performance on simulated and real data. PG-TS explores the action space efficiently and exploits high-reward arms, quickly converging to solutions of low regret. Its explicit estimation of the posterior distribution of the context feature covariance leads to substantial empirical gains over approximate approaches. PG-TS is the first approach to demonstrate the benefits of Pólya Gamma augmentation in bandits and to propose an efficient Gibbs sampler for approximating the analytically unsolvable integral of logistic contextual bandits. 

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3. A framework of zero-inflated Bayesian negative binomial regression models for spatiotemporal data

   https://doi.org/10.1016/j.jspi.2023.106098  

   He, Qing; Huang, Hsin-Hsiung (March 2024, Journal of Statistical Planning and Inference)

   Spatiotemporal data analysis with massive zeros is widely used in many areas such as epidemiology and public health. We use a Bayesian framework to fit zero-inflated negative binomial models and employ a set of latent variables from Pólya-Gamma distributions to derive an efficient Gibbs sampler. The proposed model accommodates varying spatial and temporal random effects through Gaussian process priors, which have both the simplicity and flexibility in modeling nonlinear relationships through a covariance function. To conquer the computation bottleneck that GPs may suffer when the sample size is large, we adopt the nearest-neighbor GP approach that approximates the covariance matrix using local experts. For the simulation study, we adopt multiple settings with varying sizes of spatial locations to evaluate the performance of the proposed model such as spatial and temporal random effects estimation and compare the result to other methods. We also apply the proposed model to the COVID-19 death counts in the state of Florida, USA from 3/25/2020 through 7/29/2020 to examine relationships between social vulnerability and COVID-19 deaths. 

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4. Dynamic Shrinkage Processes

   https://doi.org/10.1111/rssb.12325  

   Kowal, Daniel R; Matteson, David S; Ruppert, David (May 2019, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Summary We propose a novel class of dynamic shrinkage processes for Bayesian time series and regression analysis. Building on a global–local framework of prior construction, in which continuous scale mixtures of Gaussian distributions are employed for both desirable shrinkage properties and computational tractability, we model dependence between the local scale parameters. The resulting processes inherit the desirable shrinkage behaviour of popular global–local priors, such as the horseshoe prior, but provide additional localized adaptivity, which is important for modelling time series data or regression functions with local features. We construct a computationally efficient Gibbs sampling algorithm based on a Pólya–gamma scale mixture representation of the process proposed. Using dynamic shrinkage processes, we develop a Bayesian trend filtering model that produces more accurate estimates and tighter posterior credible intervals than do competing methods, and we apply the model for irregular curve fitting of minute-by-minute Twitter central processor unit usage data. In addition, we develop an adaptive time varying parameter regression model to assess the efficacy of the Fama–French five-factor asset pricing model with momentum added as a sixth factor. Our dynamic analysis of manufacturing and healthcare industry data shows that, with the exception of the market risk, no other risk factors are significant except for brief periods. 

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5. Granger Causal Inference from Spiking Observations via Latent Variable Modeling

   https://doi.org/10.1109/IEEECONF56349.2022.10051886  

   Khosravi, Sahar; Rupasinghe, Anuththara; Babadi, Behtash (July 2023, IEEE)

   Extracting directional connectivity in a neuronal ensemble from spiking observations is a key challenge in understanding the circuit mechanisms of brain function. Existing methods proceed in two stages, by first estimating the latent processes that govern spiking, followed by characterizing connectivity using said estimates. As such, the extracted networks in the second stage are highly sensitive to the accuracy of the estimates in the first stage. In this work, we introduce a framework to directly extract Granger causal links from spiking observations, without requiring intermediate time-domain estimation, by explicitly modeling the endogenous and exogenous latent processes that underlie spiking activity. Our proposed method integrates several techniques such as point processes, state-space modeling and Pólya-Gamma augmentation. We demonstrate the utility of our proposed approach using simulated data and application to real data from the rat brain during sleep. 

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