rank-likelihood estimation

This work addresses the challenge that existing regression methods struggle to handle arbitrary ordinal data—whether continuous or discrete—without imposing restrictive assumptions such as predefined transformation forms or distributional specifications, which limits their ability to model mean-variance relationships flexibly. To overcome this, the authors propose a monotonic transformation linear regression framework based on an extended rank likelihood, treating the mean-variance relationship as a nuisance parameter and thereby avoiding explicit specification of data type or transformation. Parameter estimation is carried out via Bayesian inference with Gibbs sampling, and conformal calibration is integrated to construct predictive intervals. Theoretical analysis and experiments demonstrate that the approach incurs no asymptotic information loss in both continuous and binary extremes and maintains valid marginal frequentist coverage even under model misspecification, achieving both estimation accuracy and prediction reliability.

This paper addresses the “weak paradox” of inverse probability weighting (IPW) estimators—highlighted by Basu (1988) and Wasserman (2004)—in survey sampling, causal inference, and Bayesian evidence estimation. We propose two Bayesian remedies: an IPW correction framework based on Bayesian sieves (binning plus nonparametric smoothing) and one built upon conjugate hierarchical models. We provide the first systematic theoretical comparison, proving posterior consistency for both under MCAR, with substantially weaker assumptions on inclusion probabilities than classical IPW. Monte Carlo simulations demonstrate that both estimators drastically reduce mean squared error in Wasserman’s counterexample. Our results extend IPW robustness to Bayesian evidence estimation and average treatment effect evaluation, offering a novel paradigm for weighted inference in high-dimensional, sparse, or non-regular settings.

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.

Conventional inference methods for slope parameters in rank-rank regression fail under distributional discontinuities; OLS estimation and its asymptotic distribution are highly sensitive to rank ties, undermining the reliability of intergenerational mobility analyses. Method: This paper establishes the first universal asymptotic theory for the OLS estimator in rank-rank regression—applicable to arbitrary distributions, including discrete ones—thereby relaxing the standard continuity assumption. It further extends the framework to multiple classes of rank-based regression models, developing confidence intervals and hypothesis tests via nonstandard asymptotic analysis and robust rank modeling. Contribution/Results: Empirically, the proposed methods substantially revise prior findings in two prominent intergenerational mobility studies, yielding more statistically valid and robust policy evaluations. The approach enhances inferential reliability in settings with ties, mass points, or mixed discrete-continuous outcomes—common in socioeconomic data—while preserving interpretability through rank-scale parameters.

Bayesian inference for finite-population surveys is challenging when sampling units exhibit complex dependencies (e.g., spatial, network, or structural) and nonresponse is nonignorable. Method: We propose a unified hierarchical modeling framework that integrates graphical models and spatial random fields to characterize multivariate dependence; formally adopts the “unapologetic Bayesian” paradigm, embedding design-based weights (e.g., Horvitz–Thompson) naturally into prior and likelihood specifications; incorporates causal ignorability analysis to ensure identifiability under missing-not-at-random (MNAR) mechanisms; and employs MCMC and variational inference for scalable computation. Contribution/Results: The framework achieves improved small-area estimation accuracy and more reliable uncertainty quantification in two empirical spatial finite-population analyses. It rigorously reconciles design-based consistency with model-based flexibility, providing theoretical guarantees for valid Bayesian inference under complex survey designs and nonignorable nonresponse.

本文提出两种贝叶斯方法解决信息抽样下的推断问题，第一种通过构建一致似然函数，第二种使用损失-似然自助法以提高稳健性。

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.

Traditional hybrid experimental designs struggle to robustly control the frequentist operating characteristics of Bayesian decisions under model misspecification and lack efficient sample size determination methods applicable to generalized posteriors. This work proposes a computationally efficient experimental design framework that requires simulations at only two sample sizes and leverages extrapolation modeling of posterior summary functions to infer performance across the entire sample size space. This approach enables identification of the minimal sample size and decision rule satisfying desired operating characteristics. It represents the first general and scalable method for sample size planning under generalized posteriors, substantially reducing computational burden while enhancing robustness to model misspecification. The method’s validity and broad applicability within Bayesian M-estimation–type experiments are demonstrated through the redesign of an adaptive clinical trial with time-to-event outcomes.

This study addresses the scalability and statistical validity bottlenecks in likelihood approximation and inference for complex simulation models by proposing a novel framework based on aggregated normalizing flow chains. Methodologically, it integrates information-theoretic formalization with sequential decision-making paradigms to construct flexible probability distributions through the sequential optimization of bijective transformation parameters. Furthermore, an empirical likelihood estimator under moment constraints is employed to iteratively update and aggregate the global flow parameters. This research establishes a surrogate model that simultaneously ensures computational feasibility and statistical power, enabling efficient parameter exploration, hypothesis testing, and uncertainty quantification. Ultimately, the proposed approach provides a reliable Bayesian inference solution for complex systems.

This study addresses the challenges of inefficient posterior estimation and difficult calibration in simulation-based inference (SBI) for models with intractable likelihoods but accessible forward simulators. We propose a sequential posterior estimation framework based on Gaussian mixture-of-experts surrogates. By leveraging localized conditional density approximations to construct proposal distributions, the method corrects the posterior via amortized ratio estimation and importance sampling. Furthermore, we introduce a localized simulation-based calibration (SBC) approach that efficiently reuses surrogates across broad neighborhoods at low computational cost. The effectiveness of this framework is validated through three case studies involving real-world epidemiological data, demonstrating substantial improvements in both the computational efficiency and inferential accuracy of SBI.