fit state-space models

This paper addresses the low sampling efficiency and slow convergence of Markov chain Monte Carlo (MCMC) methods in Bayesian inference for state-space models. We propose a novel sampling framework that integrates the forward–backward algorithm with particle MCMC. Leveraging the Markov property of latent states and conditional independence of observations, we embed latent variable sampling within a Gibbs update and employ particle filtering to approximate intractable likelihoods. A reparameterization strategy is further introduced to improve chain mixing. The method enables joint, efficient inference of latent variables and model parameters while preserving theoretical correctness. It significantly accelerates convergence and reduces effective sample autocorrelation. Experiments demonstrate robustness and computational scalability on nonlinear and non-Gaussian time-series modeling tasks. Our approach provides a practical, general-purpose solution for Bayesian inference in complex state-space models.

This study addresses the limitations of traditional state-space models, which rely on predefined nonlinear dynamics and struggle with theoretically under-specified complex systems, as well as the high computational cost of Bayesian inference in Gaussian process state-space models for moderately long sequences. To overcome these challenges, the authors propose two enhanced Gibbs sampling strategies that substantially improve sampling efficiency and convergence reliability. By integrating confirmatory factor analysis to construct an identifiable and interpretable measurement structure, they develop a comprehensive framework for learning nonlinear latent dynamical systems. Simulation studies validate the accuracy of posterior inference, while two empirical applications demonstrate the method’s practical utility and interpretability. An open-source implementation is provided, offering researchers an efficient and feasible workflow for empirical analysis.

The latent Markov modeling community suffers from fragmented formalisms, inconsistent terminology, and disparate inference methods and software tools—severely hindering practical adoption. To address this, we propose a unified latent-variable Markovian framework for time-series and sequential data, systematically integrating paradigms including hidden Markov models, state-space models, and Markov-modulated Poisson processes under a recursive structural perspective. We introduce a modular (Lego-style) modeling language and develop the efficient R package *LaMa*, whose core implements numerically stable maximum-likelihood estimation in C++ with dynamic programming, forward–backward algorithms, and optimizations for state-dependent structures. This framework substantially lowers the modeling barrier, enabling rapid, robust, and reproducible parameter estimation across all supported models. Moreover, it provides a data-driven, practical roadmap for model selection—bridging theoretical flexibility with empirical usability.

This study systematically clarifies the similarities, differences, and theoretical connections between state space models (SSMs) and hidden Markov models (HMMs) in sequence modeling. By employing a unified probabilistic graphical model framework, it compares classical probabilistic SSMs—including linear Gaussian SSMs and Kalman filtering—with HMMs and modern neural SSMs, analyzing their structural properties, inference algorithms, and learning mechanisms. The work identifies precise conditions under which these models are equivalent or fundamentally distinct, establishing formal correspondences across representation, inference, and training paradigms. In doing so, it provides a principled probabilistic interpretation of modern neural SSMs, bridges conceptual gaps among control theory, probabilistic modeling, and deep learning, and offers theoretical guidance for informed model selection and design.

Existing probabilistic programming languages lack native support for dynamic systems—particularly state-space models—hindering the broader adoption of Bayesian methods in this domain. This work introduces dynestyx, a library that provides first-class, unified, and user-friendly support for state-space models within a probabilistic programming framework. dynestyx enables flexible specification of priors, accommodates both discrete- and continuous-time dynamics, handles mixed-effects data, and facilitates joint Bayesian inference over latent states and model parameters with full uncertainty quantification. By doing so, this contribution substantially enhances the accessibility, flexibility, and practical utility of dynamic system modeling across statistics, signal processing, and machine learning.

This study addresses a key limitation of traditional latent-variable state-space models, which assume process noise is independent of the latent state and thus fail to capture state-dependent stochastic fluctuations commonly observed in biological and behavioral systems. To overcome this, the authors propose a state-coupled stochastic volatility framework that introduces a coupling parameter γ, allowing the variance of the latent process to dynamically scale with the deviation from an underlying latent equilibrium point. This work presents the first approach to modeling and identifying such coupling between latent states and process noise variance under partial observability. An efficient particle expectation-maximization algorithm, integrating guided particle filtering with backward trajectory smoothing, is developed for parameter estimation. Simulations demonstrate that the method substantially reduces parameter estimation bias under strong coupling and high observation noise, confirming its efficacy and robustness.

This work proposes a Bayesian dynamic latent space model tailored for weighted temporal networks exhibiting complex characteristics such as integer-valued edge weights, zero-inflation, dynamically evolving node latent positions, and time-varying sparsity. The model captures the temporal dependencies of node latent features through vector autoregression and, for the first time in latent space network modeling, incorporates both contemporaneous and lagged dependencies across nodes and latent dimensions. To enhance inference efficiency, a non-recursive block-updating multi-step sampler is developed, integrating auxiliary mixture sampling, Laplace approximation, and partially collapsed Gibbs sampling to substantially improve Markov chain mixing and computational scalability. The framework flexibly accommodates both integer and continuous edge weights and can be readily extended to static or dynamic settings, enabling accurate and efficient inference for complex temporal networks.

This work addresses the issue of overconfident filtering in nonlinear state-space models caused by misspecification in either the dynamics or observation model. To mitigate this, the authors propose a Prediction-oriented (PrO) online filtering approach that does not strictly rely on Bayes’ theorem but instead learns only when the overall model is correctly specified. By integrating a linear-Gaussian approximation, the method establishes an efficient iterative update mechanism, yielding a variant of the extended Kalman filter termed EKF-PrO. This framework requires no hyperparameters, is computationally efficient, and automatically adapts to model misspecification. Experimental results demonstrate that, across various scenarios involving both linear and nonlinear model misspecifications, EKF-PrO achieves substantially improved inference robustness while maintaining computational costs comparable to existing methods.

This work proposes a probabilistic inference framework that integrates inductive biases to address the challenges of uncertainty quantification in deep sequential models. While traditional Bayesian approaches struggle with prior specification and inference accuracy in large-scale networks, the proposed method establishes a theoretical connection between Transformer attention mechanisms and sparse Gaussian processes, enabling scalable approximate Bayesian inference. It introduces cross-domain inducing points derived from HiPPO operators to support long-range historical modeling in online learning settings. Furthermore, self-supervised signals are leveraged to enrich the probabilistic structure of latent variables in sequence generation. The resulting approach significantly enhances the uncertainty quantification capability, probabilistic expressiveness, and scalability of deep sequential models, all while maintaining competitive predictive performance.