bayesian time-series causal estimation

This paper addresses the challenge of modeling causal dose–response relationships between time-varying continuous exposures (e.g., dynamic dosing trajectories) and longitudinal outcomes. We propose the first scalable nonparametric Bayesian framework for this purpose. Methodologically, it innovatively integrates a two-level nonparametric generalized Bayesian bootstrap with generalized estimating equations (GEE), incorporates generalized propensity score modeling and inverse probability weighting, and employs a Dirichlet process prior to flexibly characterize the exposure–effect function—without assuming a prespecified functional form—while accommodating temporal dependence and dynamic confounding. The framework enables causal effect estimation at arbitrary exposure levels. Empirically, applied to panel data on monthly metro ridership and COVID-19 case growth across multiple cities, it identifies a statistically significant positive causal dose–response relationship between ridership increases and accelerated case growth, demonstrating both methodological validity and practical utility.

Real-world causal discovery frequently encounters challenges posed by cyclic causal structures and latent confounders; however, most existing methods assume acyclic graphs and no unmeasured confounding, leading to unreliable identification. To address this, we propose BayCausal—the first fully Bayesian framework capable of identifiable causal structure learning under simultaneous presence of cycles and latent confounders. BayCausal integrates identifiability theory from noise-independent component analysis with recent advances in factor modeling, thereby overcoming classical identifiability limitations. We release the first open-source R package—BayCausal—designed specifically for such complex settings. Extensive simulations demonstrate that BayCausal significantly outperforms state-of-the-art methods. Applied to an HIV dataset, it successfully uncovers clinically meaningful cyclic causal mechanisms, validating both its statistical efficacy and practical utility in real-world biomedical applications.

Conventional causal inference methods, designed for discretized time and finite-dimensional assumptions, fail to handle infinite-dimensional treatment–confounder feedback in functional longitudinal data—where outcomes, treatments, and confounders are observed as continuous-time trajectories—as arises in real-time health monitoring. Method: We integrate stochastic process theory, measure theory, and net convergence into causal identification, systematically generalizing g-computation, inverse probability weighting (IPW), and doubly robust formulae to accommodate time-varying outcomes subject to censoring and truncation by death. Contribution/Results: This work establishes the first nonparametric causal identification framework for functional longitudinal data, providing rigorous theoretical foundations for causal effect estimation without parametric or dimensionality constraints. Simulation studies validate its effectiveness, filling a critical theoretical gap and enabling future development of nonparametric causal estimators for functional data.

Existing causal inference methods are constrained by assumptions of low-dimensional, static confounders and single-action interventions, limiting their ability to model high-dimensional confounding and sequential interventions. This paper introduces the first general-purpose causal inference framework based on deep autoregressive models (e.g., Transformers). It employs a causal DAG-guided serialization scheme to encode structured causal data into token sequences, enabling unified estimation of intervention probabilities, counterfactual outcomes, and other causal quantities. Its core innovation is the first integration of the autoregressive paradigm into causal inference—supporting end-to-end, joint estimation of multiple causal targets within a single model, without reliance on low-dimensional or static confounding assumptions. Empirical evaluation across three diverse tasks—maze navigation, chess endgame solving, and academic keyword impact assessment—demonstrates substantial improvements in intervention prediction accuracy and causal reasoning efficiency.

This paper addresses individual-time-point-level counterfactual inference under adaptive treatment strategies in multi-unit, multi-period sequential experiments, aiming to relax strong prior assumptions on intervention policy structure. We propose a nonparametric latent factor model that unifies nonlinear mixed-effects and bilinear factor models. Integrating nonparametric nearest-neighbor estimation with sequential experimental design, we derive the first non-asymptotic, high-probability error bound for individual-time-point-level counterfactual means. We establish theoretical consistency of the estimator and asymptotic validity of associated confidence intervals. The method is validated via simulations and the HeartSteps mobile health clinical trial, demonstrating both statistical accuracy and practical utility. Our core contribution lies in breaking the traditional reliance on restrictive parametric or structural assumptions about treatment policies—enabling high-precision, assumption-light, fine-grained causal inference at the individual-time-point level.

Estimating causal effects from high-dimensional binary time series is highly challenging in the presence of temporal dependencies, interference across units, and latent confounders. This work proposes the first causal inference framework that integrates a dynamic Ising model with a low-rank latent factor structure to jointly capture complex interference patterns and unobserved confounding. The model parameters are efficiently learned via maximum pseudolikelihood estimation, and non-asymptotic statistical theory is established to guarantee estimation consistency—even from a single observed trajectory. By unifying the modeling of interference and latent confounding within one sample, the method substantially improves estimation accuracy. Empirical evaluations on both synthetic data and a real-world application—assessing the effect of county-level vaccination rates on COVID-19 mortality in the United States—demonstrate the effectiveness of the proposed approach.

This study addresses the challenge of evaluating the extent to which dynamic surrogate markers explain the treatment effect on a primary outcome in longitudinal settings. Building upon the potential outcomes framework, it proposes the first causal evaluation method specifically designed for longitudinal surrogate markers. The approach employs a state-space model combined with Kalman filtering and smoothing to efficiently estimate the time-varying proportion of treatment effect explained by the surrogate. To enhance inferential robustness, the method integrates a nonparametric bootstrap strategy and a test for temporal homogeneity of surrogate efficacy. Simulation studies and an application to a diabetes clinical trial demonstrate that the proposed method performs well even with limited sample sizes, offering a reliable and interpretable causal quantification tool for assessing the validity of longitudinal surrogate markers.

This study addresses the challenge of estimating time-varying treatment effects in mobile health micro-randomized trials, where repeated interventions influence both longitudinal outcomes and recurrent events. The authors propose an innovative joint longitudinal-survival modeling framework that, for the first time, incorporates time-varying treatment effects from micro-randomized trials into a unified joint model. By leveraging Bayesian inference, the approach flexibly captures dynamic associations among repeated treatments, multidimensional longitudinal markers, and recurrent event times, while accommodating diverse treatment effect mechanisms. Model selection is guided by information criteria, and the performance of the survival submodel is evaluated using calibration plots. Simulation studies and an analysis of a substance use micro-randomized trial demonstrate that the proposed method achieves excellent model fit and accurate estimation of treatment effects.

This study addresses the challenges of estimating causal treatment effects within predefined subgroups, where sparse samples, unstable covariate distributions, and right censoring often lead to high bias and uncertainty. The authors propose a novel approach that extends hierarchical Bayesian bootstrap (HBB) to time-to-event causal subgroup analysis with right-censored data. By integrating a Bayesian accelerated failure time model with a nonparametric hierarchical prior, the method models subgroup-specific baseline covariate distributions while borrowing strength across subgroups. Joint uncertainty from both the survival model and covariate distribution is propagated via the posterior g-formula. Simulation studies demonstrate that the proposed method substantially improves estimation stability and accuracy across varying levels of sparsity and censoring, outperforming existing alternatives such as Bayesian additive regression trees.

Existing time series benchmarks lack interventional data, hindering the training of causal foundation models. To address this gap, this work proposes CausalTimePrior, a framework that introduces the first synthetic time series structural causal model (TSCM) capable of generating paired observational and interventional data. The framework supports configurable causal graphs, nonlinear autoregressive mechanisms, state-switching dynamics, and diverse intervention types—including hard, soft, and time-varying interventions. Prior-data fitting networks (PFNs) trained within this framework demonstrate effective in-context estimation of causal effects on unseen TSCMs, underscoring the framework’s pivotal role in advancing causal foundation models for time series.