imprecise dirichlet inference

本文提出了一种非参数贝叶斯推理框架，用于解决部分识别的离散响应模型问题，通过直接对条件概率质量函数进行推理，避免了将条件矩转换为无条件矩或离散化协变量的需求。

本文提出了一种贝叶斯框架，用于处理多层数据生成过程中的模型误设问题，通过半参数方法估计总体参数并考虑集群和单元级别变化。

This study addresses the limitations of traditional Markov queueing models in health economics, which rely on precisely specified transition matrices that are often not uniquely identifiable from available data, thereby undermining decision robustness. The authors introduce a set of evidence-compatible transition matrices and formulate a finite-horizon Markov queueing model under imprecise probabilities, marking the first application of imprecise probability methods to cumulative health economic outcomes. Under row-wise independence and compactness assumptions, they develop an efficient computational approach for bounding expected outcomes using Bellman-type upper and lower transition operators combined with an imprecise Dirichlet model, and establish corresponding envelope and consistency theorems. Applied to a cost-effectiveness analysis of patent foramen ovale closure, the proposed method reveals that the net monetary benefit interval straddles zero—contrasting with the modest support for intervention suggested by conventional methods—and highlights substantial sensitivity of policy decisions to unidentified transition probabilities.

To address inadequate calibration of both local (e.g., group-level random effects) and global parameters in multilevel Bayesian models under complex survey designs, this paper proposes an improved survey-weighted pseudo-posterior framework with an automated post-processing pipeline—enabling, for the first time, consistent uncertainty calibration for both parameter types within hierarchical structures. The method integrates mixed-effects modeling, weighted likelihood construction, and posterior reweighting calibration, ensuring asymptotic consistency theoretically and seamless compatibility with mainstream Bayesian software computationally. Simulation studies and empirical analysis using the National Survey on Drug Use and Health (NSDUH) demonstrate that the proposed approach substantially improves estimation accuracy and reliability of uncertainty quantification, particularly reducing bias in random-effects inference. The corresponding algorithms are publicly available and integrated into the R package `csSampling`, offering a scalable, reproducible solution for hierarchical Bayesian analysis under complex sampling.

This paper addresses inference for partially identified parameters in incomplete models. We propose a unified inferential method that simultaneously achieves robustness to model misspecification and information efficiency. Our core innovation is the first construction of a Kullback–Leibler (KL) information criterion that jointly accommodates both incompleteness and misspecification robustness, yielding a nonempty, identifiable set of pseudo-true parameters. The method fully exploits information from both discrete and continuous covariates and enables computationally tractable inference via an asymptotically pivotal Rao score statistic. We establish theoretical consistency and asymptotic normality under both correct specification and misspecification. Compared to existing approaches, our framework substantially enhances the reliability and applicability of partial identification inference, providing the first unified inferential framework for incomplete models with set-valued predictions that is both theoretically rigorous and practically implementable.

This study investigates the frequentist validity of two-step (plug-in) approaches in semiparametric Bayesian inference, with particular emphasis on settings involving nuisance parameters. For models satisfying Neyman orthogonality conditions, the authors demonstrate that marginal posteriors for the target parameter retain desirable frequentist properties—even when uncertainty in estimating the nuisance parameters is ignored—by effectively severing feedback between the nuisance and target parameters. The analysis is further extended to non-orthogonal settings, where posterior asymptotic robustness is guaranteed under mere consistency of the nuisance parameter estimator. Methodologically, the framework combines Dirichlet processes with Bayesian bootstrap techniques for nonparametric modeling and is applied to plug-in estimation of propensity scores in causal inference, showing that the plug-in step exerts negligible influence on the resulting posterior for the target parameter.

This study addresses the underestimation of variance and inferential bias in synthetic data arising from informative sampling and missing data in complex surveys. The authors propose a Bayesian synthesis framework that simultaneously imputes missing values and generates synthetic data through an adaptive weighting mechanism. By integrating principles of informative sampling theory within a Bayesian modeling paradigm, the method ensures consistent parameter estimation while yielding an asymptotically efficient Godambe information matrix. This overcomes the systematic underestimation of uncertainty inherent in conventional Bayesian synthesis approaches. Simulation studies demonstrate that the proposed method accurately quantifies uncertainty for both model parameters and population-level inferences, substantially enhancing the statistical reliability of synthetic datasets.

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 work addresses the non-uniform distribution of posterior predictive p-values (ppp) under the Bayesian framework, which hinders reliable model diagnostics and cross-model comparisons. The authors propose a natural calibration method that transforms ppp values into calibrated posterior predictive p-values (cppp), which follow a standard uniform distribution under the true model. This calibration establishes, for the first time, a unified and comparable scale for ppp-based assessments. The approach is grounded in a double-simulation computational framework that seamlessly integrates Bayesian inference with posterior predictive checking, and it is applicable to both parametric and nonparametric models. Theoretical analysis demonstrates favorable statistical properties of cppp, while empirical studies illustrate its effectiveness in enabling fair comparisons among models and prior specifications on real-world data.

The Hierarchical Dirichlet Process (HDP) provides a flexible Bayesian nonparametric framework for modeling grouped data with a shared yet unbounded collection of mixture components. While existing applications of the HDP predominantly focus on the Dirichlet-multinomial conjugate structure, the framework itself is considerably more general and, in principle, accommodates a broad class of conjugate prior-likelihood pairs. In particular, exponential family distributions offer a unified and analytically tractable modeling paradigm that encompasses many commonly used distributions. In this paper, we investigate analytic results for two important members of the exponential family within the HDP framework: the Poisson distribution and the normal distribution. We derive explicit closed-form expressions for the corresponding Gamma-Poisson and Normal-Gamma-Normal conjugate pairs under the hierarchical Dirichlet process construction. Detailed derivations and proofs are provided to clarify the underlying mathematical structure and to demonstrate how conjugacy can be systematically exploited in hierarchical nonparametric models. Our work extends the applicability of the HDP beyond the Dirichlet-multinomial setting and furnishes practical analytic results for researchers employing hierarchical Bayesian nonparametrics.