bayesian nonparametric joint modelling

This study addresses missing data in bivariate longitudinal settings arising from non-random dropout—particularly when the two response variables exhibit asynchronous dropout times and complex distributional features such as skewness and heavy tails. The authors propose an innovative Bayesian nonparametric joint modeling approach that simultaneously characterizes the observation processes and dropout mechanisms for both variables. By incorporating identification constraints based on dropout indicators and sensitivity parameters, the method achieves partial identification of the missing data distribution under nonignorable missingness. Assigning priors to the sensitivity parameters enables systematic sensitivity analyses across a range of plausible missingness scenarios. This work represents the first extension of Bayesian nonparametric modeling to bivariate longitudinal dropout contexts and demonstrates its practical utility through successful application to a cost-effectiveness clinical trial on intellectual disability interventions, yielding robust evidence to inform health policy decisions.

This paper addresses the challenge in Bayesian nonparametric survival analysis where priors depend on stochastic sources and must adapt dynamically with incoming data. Methodologically: (1) it introduces, for the first time, a sequence of random hyperparameters to construct a time-varying prior mechanism that is provably consistent and satisfies the Bernstein–von Mises theorem; (2) it designs a hybrid time-varying ordering mechanism to model the cumulative hazard function, enabling exact path simulation from Beta Lévy processes; (3) it proposes a novel nonparametric distribution stitching model that jointly characterizes both the bulk and the tail of the distribution. Theoretical contributions include rigorous proofs of Bayesian consistency and asymptotic normality. Algorithmically, it provides an efficient posterior path sampling scheme. Empirical evaluation on real survival datasets demonstrates substantial improvements in full-distribution calibration—particularly for heavy-tailed behavior—over existing methods.

To address statistical efficiency loss and standard error bias arising from the conventional two-stage approach—first estimating marginal distributions nonparametrically/semiparametrically, then fitting a Gaussian copula—in modeling multivariate non-normal data, this paper proposes an integrated likelihood framework that jointly estimates marginal distributions and Gaussian copula parameters. Key contributions include: (i) the first formal definition of four classes of nonparametric normal log-likelihood functions; (ii) identification and exploitation of the biconvex structure of the objective function, enabling a convex approximation optimization strategy; and (iii) derivation of exact score functions via the Genz algorithm, facilitating first-order optimization. The method substantially enhances robustness of transformation-based discriminant analysis for limit-of-detection biomarker data and improves asymptotic efficiency and standard error accuracy in semiparametric polychoric correlation estimation.

This paper addresses doubly robust estimation of the functional mean conditional on covariates when functional data are subject to random missingness. Under the assumption that the missingness mechanism depends only on observed covariates, we propose two semiparametric doubly robust estimators—one integrating inverse probability weighting and the other regression adjustment. We establish, for the first time, their Gaussian process limiting distributions and derive explicit covariance functions. The proposed methods enable construction of simultaneous confidence bands with asymptotically exact coverage. We rigorously prove the double robustness and asymptotic normality of the estimators. Monte Carlo simulations demonstrate their finite-sample superiority over competing approaches. An empirical application to counterfactual functional mean inference illustrates their utility in functional causal inference, delivering both theoretical guarantees and practical applicability.

This study addresses the challenge of quantifying uncertainty in survival analysis arising from censored data, small sample sizes, and population heterogeneity. The authors propose a model-agnostic Bayesian framework that circumvents reliance on a full likelihood specification and avoids sensitivity to parametric distributional assumptions. The approach integrates Bayesian bootstrapping with generalized Bayesian (Gibbs) posterior updating: nonparametric survival estimates are generated via Dirichlet-weighted resampling to capture sampling uncertainty, while prior information is incorporated through a loss-based updating rule to yield robust posterior inference. The framework is compatible with the Cox proportional hazards model, preserving the interpretability of hazard ratios. Simulation studies and real-data applications demonstrate its ability to effectively quantify uncertainty and flexibly leverage prior knowledge. An accompanying open-source R package, BayesBoots, has been released.

This study addresses the limitations of traditional joint models in clinical longitudinal studies, where repeatedly measured biomarkers or quality-of-life outcomes are often associated with event times but constrained by the proportional hazards assumption, hindering interpretability on the time scale. The authors propose a class of Bayesian semiparametric accelerated failure time joint models that integrate linear mixed-effects models for the longitudinal process and employ Bernstein polynomials to flexibly model the baseline hazard. A time-warping rescaling strategy is introduced to enhance numerical stability and parameter identifiability. By relaxing the proportional hazards assumption, the proposed approach offers more intuitive time-scale interpretations. Simulation studies demonstrate that, when event risk depends on underlying longitudinal trajectories, the method yields more accurate estimates of treatment effects compared to separate modeling approaches and exhibits excellent finite-sample performance.

This study addresses fundamental theoretical and applied challenges at the intersection of Bayesian statistics and nonparametric methods, offering a systematic synthesis and extension of the research trajectory in nonparametric Bayesian inference. By incorporating stochastic process priors and rigorous theoretical analysis, the work develops a modeling framework tailored to highly structured random systems. Beyond providing a comprehensive review of core advances in the field, it highlights several emerging directions that address gaps in earlier literature. The resulting contributions significantly advance both the theoretical foundations and practical applicability of nonparametric Bayesian methodologies, thereby strengthening their role in modern statistical modeling and inference.

This study addresses Bayesian inference for low-dimensional target parameters in semiparametric models, particularly under the presence of complex nuisance components that may compromise frequentist properties. To this end, we construct posterior distributions by integrating estimating function methods with nonparametric Bayesian techniques—such as Dirichlet processes and Bayesian bootstrap—under conditions weaker than the classical stochastic equicontinuity assumption. We establish asymptotic normality and consistency of the resulting posterior, rigorously identifying the key assumptions required to guarantee desirable frequentist behavior. The theoretical analysis systematically elucidates how relaxing these assumptions affects inferential performance. Extensive simulations corroborate the effectiveness of the proposed methodology, demonstrating its robustness and accuracy in practical settings.

This study addresses the nonignorable nonrandom missingness arising from self-censoring in longitudinal studies, particularly when later responses depend on prior observations. It introduces, for the first time, two classes of graphical-model-based missing mechanisms that enable identification of the full-data distribution under rank or completeness conditions. A two-stage Vuong-type selection procedure is proposed: first testing for observable distinguishability between candidate models, then selecting the preferred model based on Kullback–Leibler divergence to ensure asymptotic validity of Wald inference under the chosen model. The framework jointly guarantees model distinguishability and selection consistency, demonstrates robust performance in simulations, and is successfully applied to Job Corps data, yielding a principled choice of missing mechanism and reliable estimation of functional parameters.