post-bayesian ipw

This study addresses the challenge of accurate parameter estimation in Bayesian inference when selection bias and systematic bias are present. The authors propose a generalized Bayesian approach that, for the first time, integrates inverse probability weighting (IPW) into the Bayesian framework. By interpreting IPW as a reweighting of the Kullback–Leibler divergence between the model and the true data-generating mechanism, they construct a posterior distribution that simultaneously inherits the bias-correction properties of frequentist IPW and maintains Bayesian coherence. Theoretical analysis establishes favorable asymptotic convergence properties of the proposed posterior. Empirical validation on both simulated data and a large-scale prostate cancer registry dataset—used to predict mortality based on PSA levels—demonstrates the method’s effectiveness, substantially extending the applicability of Bayesian inference to settings with biased observations.

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.

In PAC-Bayes theory, conventional sequential prior updates discard confidence information tied to historical data volume, undermining both theoretical rigor and practicality in multi-stage learning. This work introduces the first lossless recursive PAC-Bayes framework. Methodologically, it (1) proposes a novel paradigm of prior-loss scaling and excess-loss decomposition, enabling composable, zero-information-loss confidence bounds across stages; (2) generalizes the split-kl inequality to discrete random variables, yielding a recursive PAC-Bayes-split-kl bound; and (3) provides theoretical guarantees that fully preserve confidence characterizations over all historical data. Empirically, the method achieves significantly tighter generalization bounds and superior model selection performance compared to state-of-the-art approaches.

This work addresses the slow MCMC convergence in Gibbs posterior sampling under stochastic loss functions, which stems from spurious dependence on the number of pseudo-observations. We propose the first pseudo-sample-size–independent corrected piecewise deterministic Markov process (PDMP) sampler. By designing a novel jump-rate function and direction mechanism, our method rigorously ensures that the invariant measure remains invariant to the pseudo-observation count—thereby overcoming the inherent trade-off between asymptotic bias and slow convergence in conventional stochastic-loss inference. We prove that the sampler converges exactly to the target Gibbs posterior measure with a uniform convergence rate independent of pseudo-sample size. Empirical validation across three canonical settings—likelihood-intractable models, misspecified models, and stochastic losses—demonstrates elimination of pseudo-sample-size bias in posterior sampling, alongside substantial improvements in robustness and estimation accuracy.

Traditional Gibbs posteriors suffer from poor support in high dimensions, difficulty balancing computational efficiency with constraint modeling, and systematic underestimation of uncertainty due to partial optimization over latent variables. Method: We propose the “bridging posterior” framework, which embeds optimization subproblems directly into Bayesian modeling and employs conditionally deterministic latent variables for efficient parameter inference. Contribution/Results: This work establishes the first optimization-driven generalized Bayesian paradigm; we prove that the √n-calibrated bridging posterior is asymptotically equivalent to the classical integrated posterior, thereby resolving the long-standing misconception about uncertainty underestimation. By unifying convex/non-convex optimization, profile likelihood, and variational principles, we design a differentiable latent-variable generative model. Empirically, the framework significantly improves inference accuracy and robustness—demonstrated on maximum-margin classification, latent Gaussian models, and multi-network joint analysis—while retaining optimization-level computational efficiency.

Under model misspecification, conventional Bayesian inference yields posterior credible sets with inadequate uncertainty quantification due to the failure of the information identity. This work addresses the learning rate calibration problem in generalized Bayesian inference by proposing an optimization criterion based on the weighted Fisher divergence. The proposed approach derives a closed-form solution for the learning rate by minimizing the discrepancy between the asymptotic distribution of the generalized posterior and a normal distribution with sandwich covariance. This solution encompasses the Fisher information-matching learning rate as a special case and is shown to be no greater than this benchmark in important scenarios. Theoretical analysis, supported by numerical experiments and real-data applications, demonstrates the superior performance of the proposed method in posterior calibration and uncertainty quantification.

This study addresses the limitation that the conventional Bayesian Information Criterion (BIC) cannot be directly applied to model selection under reweighted distributions in causal inference. To overcome this, we propose a generalized BIC extended to reweighted distribution settings, enabling the accurate identification of direct causes within marginal structural models. We theoretically establish the asymptotic consistency of the proposed method in the presence of unmeasured confounders and weight estimation errors. Simulation experiments demonstrate that the proposed reweighted BIC exhibits favorable asymptotic properties and significantly outperforms existing alternative methods, achieving precise selection of direct causes.

This study addresses the bias in causal effect estimation arising from misspecification of the propensity score model in inverse probability weighting (IPW). To mitigate this issue, the authors propose two clustering-informed strategies: a cluster-augmented IPW approach and a global propensity score model incorporating cluster membership indicators. The robustness of these methods is systematically evaluated through Monte Carlo simulations and an empirical analysis of breast cancer data across varying sample sizes and model specifications. Results demonstrate that the proposed clustering-aware methods substantially reduce both estimation bias and mean squared error, particularly when latent subgroup structures are present. Furthermore, they enable subgroup-specific causal effect estimation and significantly enhance robustness against propensity score model misspecification.

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。

In Bayesian sequential inference, the marginal likelihood is often treated as a static constant, overlooking its role in modulating the pace of belief updates. This work reveals that the marginal likelihood not only governs the magnitude of individual updates but also encodes frequency patterns embedded in historical data, which the authors reformulate as a dynamic regularizer. By introducing three diagnostic metrics to control online estimation gain and integrating prior and posterior distributions into a hybrid probabilistic mechanism, the proposed approach adaptively adjusts to distributional drift. The resulting framework unifies Bayesian updating with frequentist characteristics within a two-layer probabilistic architecture, substantially enhancing the robustness of sequential estimation and offering a novel paradigm for online risk quantification.