bayesian time-series model comparison

Existing diffusion-based time-series modeling approaches rely on fixed Gaussian priors, which inadequately capture temporal dynamic structures and thus limit generation quality. To address this, we propose TSFlow—the first conditional probabilistic forecasting model that integrates Conditional Gaussian Processes (CGPs) into the flow matching framework. TSFlow constructs data-dependent dynamic priors via optimal transport paths and introduces a novel conditional prior sampling mechanism, enabling the generative process to better reflect intrinsic temporal correlations and uncertainty. Crucially, it supports high-fidelity unconditional generation and flexible conditional forecasting without modifying the training objective. Evaluated on eight real-world datasets, TSFlow achieves significant improvements in unconditional generation metrics over state-of-the-art methods and attains either SOTA or leading performance across multiple probabilistic forecasting benchmarks.

This project addresses the inverse problem of spatiotemporal mechanistic models under noisy observations, aiming to robustly learn dynamic mechanisms from low-quality data and efficiently interpolate system responses for arbitrary inputs. We propose a dynamic Bayesian learning framework: (i) a tractable hierarchical matrix-normal–Wishart prior enabling closed-form posterior inference, thereby avoiding MCMC sampling and variational iterations; (ii) the first dynamic Bayesian transfer learning architecture, scalable to large-scale spatiotemporal surrogate modeling; and (iii) a unified integration of Gaussian process regression, hierarchical state-space models, and Bayesian surrogate modeling to jointly enforce data-driven observation constraints and physics-based priors. Evaluated on nonlinear ODE/PDE inversion and graph-structured black-box systems, our approach significantly improves parameter estimation accuracy, state reconstruction robustness, and computational efficiency.

Bayesian modeling of large-scale spatiotemporal count data is hindered by the non-conjugacy between standard log-Gaussian process priors and Poisson likelihoods, leading to inefficient variational inference or MCMC. Method: We propose an Auto-Regressive Gamma Process (ARGP)-based fully conjugate framework that induces a temporally stationary and spatially sparse spatiotemporal structure, ensuring exact conjugacy between the latent process prior and Poisson observations. This enables efficient Gibbs sampling with linear computational complexity. By decomposing Poisson latent variables and modeling them via ARGP, the approach achieves both interpretability and scalability. Results: Experiments on synthetic and real-world datasets demonstrate substantial improvements in parameter estimation accuracy, posterior convergence speed, and out-of-sample predictive performance—particularly for generalization to novel spatiotemporal locations.

This paper addresses dynamic variable selection in high-dimensional time-varying regression with pre-specified group structures. We propose a scalable variational Bayesian framework, the first to integrate variational inference into this setting. Our method jointly incorporates dynamic sparsity-inducing priors—encompassing both group-wise sparsity and time-varying shrinkage—high-dimensional time-series modeling, and efficient approximate posterior computation. It achieves a favorable balance between statistical accuracy and computational scalability, making it suitable for large-scale macroeconomic forecasting tasks, such as inflation modeling. In extensive simulations and empirical analyses using real macroeconomic data, the method delivers substantial improvements in both point and density forecasting accuracy. Moreover, it uncovers economically interpretable, time-varying, and group-structured patterns among inflation drivers—revealing how key determinants evolve and cluster over time.

This paper addresses online changepoint detection in nonstationary univariate time series. We propose a Bayesian online method that jointly models time-varying variance and autocorrelation structure within an arbitrary-order autoregressive (AR(p)) framework with time-varying parameters. Our key contributions are: (i) the first integration of time-varying volatility and dynamic autocorrelation into a unified Bayesian changepoint detection framework; and (ii) a scoring-rule-driven recursive parameter update mechanism that preserves memory-aware modeling while enhancing real-time responsiveness. Inference is performed online via the posterior distribution of the current segment length, eliminating the need for fixed sliding windows or offline retraining. Extensive evaluation on real-world datasets across multiple domains demonstrates significant improvements in changepoint localization accuracy and short-term forecasting performance, particularly in capturing complex temporal dependencies and nonstationary evolutionary patterns.

Bayesian inference remains challenging for statisticians and learners due to conceptual ambiguities in its philosophical foundations, difficulties in prior specification, and computational complexity. Method: This paper provides a rigorous yet accessible pedagogical framework for Bayesian inference, systematically integrating core components—including Bayes’ theorem, prior modeling, posterior inference, Bayesian hypothesis testing via Bayes factors, and predictive analysis—while clarifying fundamental distinctions from frequentist paradigms in identifiability, asymptotic theory, and decision-theoretic concepts (e.g., loss functions, credible intervals). It bridges analytical derivations with modern simulation techniques such as MCMC, using canonical statistical models as unifying exemplars. Contribution/Results: The framework innovatively connects foundational concepts to advanced topics—including hierarchical modeling, nonparametric Bayesian methods, and spatiotemporal analysis—and has been successfully applied in political science, network analysis, and spatial statistics, substantially lowering the barrier to learning and applying Bayesian methods in practice.

This work proposes a dynamic Bayesian framework endowed with a Markovian dependency structure to address the challenges of computational inefficiency and limited cross-temporal information sharing in high-dimensional multivariate spatiotemporal modeling. By integrating matrix-variate Gaussian distributions, dynamic linear models, and Bayesian predictive stacking—augmented with an adaptive Markov transition mechanism—the approach enables efficient online forward filtering and backward smoothing within a sequence-parallel hybrid architecture. The proposed method achieves exact inference while substantially enhancing scalability and dynamic adaptability, making it well-suited for large-scale, multivariate, and dynamically evolving spatiotemporal data streams requiring efficient online learning.

This study addresses the challenges in modeling global and local effects within inhomogeneous pairwise interaction Gibbs point processes and the lack of effective methods for testing complete spatial randomness (CSR). To overcome these limitations, the authors propose a hierarchical Bayesian framework that, for the first time, integrates basis function expansions with Bayesian hierarchical modeling to flexibly characterize both the intensity and interaction functions. Building on posterior inference, they develop a Bayesian testing procedure specifically designed for CSR assessment. The approach enables efficient inference via Markov chain Monte Carlo (MCMC) and demonstrates strong empirical performance: when applied to water strider distribution and forest fire data, it successfully uncovers complex spatial dependence structures and provides reliable CSR tests, substantially enhancing the flexibility and inferential power of Gibbs point process modeling.

Traditional Bayesian modeling relies on model selection to balance complexity and generalization, yet this approach often compromises predictive performance in small-sample settings. This work proposes a “predictive consistency prior” that maintains stability in the prior predictive distribution as model complexity increases, thereby circumventing explicit model selection. By shifting the modeling focus from parameter sparsity to constructing reasonable and stable priors in predictive space, the method reveals that the perceived necessity of model selection fundamentally stems from inadequate prior specification. The authors implement this prior in Bayesian linear and logistic regression, forward variable selection, and nonlinear models, demonstrating through numerical experiments that flexible models equipped with the predictive consistency prior match or even outperform carefully selected simpler models in out-of-sample prediction across a range of tasks.