binary outcome modeling

This study addresses the limitations of traditional mortality models in adequately capturing dispersion patterns—such as overdispersion or underdispersion—in death count data, which hinders accurate characterization of variability. To overcome this, the authors introduce the Conway–Maxwell–Poisson (CMP) distribution into a Bayesian stochastic mortality modeling framework for the first time, treating the dispersion parameter as an unknown quantity. By assigning a Gamma prior, the approach coherently integrates parameter, process, and distributional uncertainties within a unified inferential structure, with posterior inference conducted via Markov chain Monte Carlo (MCMC) methods. The resulting model flexibly accommodates underdispersed, equidispersed, and overdispersed scenarios. Empirical analysis using male mortality data from England and Wales demonstrates that the proposed model significantly outperforms conventional Poisson and negative binomial models in both goodness-of-fit and predictive accuracy, with particularly pronounced advantages in overdispersed settings.

This study addresses the limitations of conventional frequentist approaches in effectively incorporating prior knowledge, which constrains adaptive decision-making and reliability in clinical trials. The authors propose a Bayesian framework tailored for discrete probability distributions—such as binomial, Poisson, and negative binomial—to model binary responses and overdispersed clinical endpoints using Bayesian networks. By continuously integrating accumulating evidence, the framework dynamically optimizes trial design and evaluation. Compared to maximum likelihood estimation, this approach demonstrates greater flexibility and robustness in both inferential behavior and practical performance, substantially enhancing decision quality while mitigating misinterpretation of results and reproducibility challenges.

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.

This study addresses misclassification in sensitive binary outcomes—such as self-reported intimate partner violence—arising from underreporting and other reporting errors. It proposes the first Bayesian quantile regression framework that explicitly incorporates a misclassification mechanism by introducing a latent true response variable to model both false-negative and false-positive errors. A novel Markov chain Monte Carlo (MCMC) algorithm is developed for estimation, enabling unbiased inference on covariate effects across the entire conditional distribution. Simulation studies and empirical analysis demonstrate that the proposed method substantially outperforms conventional models that ignore misclassification. When applied to intimate partner violence data, the approach reveals pervasive underreporting and shows that correcting for misclassification can materially alter substantive conclusions, thereby highlighting its practical relevance and methodological innovation.

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 incoherence commonly observed in cause-specific mortality models, where predicted deaths by cause often fail to sum to the total number of deaths. To resolve this, the authors propose a hierarchical probabilistic framework that, for the first time, integrates a Poisson–Dirichlet–multinomial structure into mortality modeling: a Poisson distribution models the total death count, a Dirichlet distribution captures the proportions of causes of death, and a multinomial distribution generates cause-specific death counts, thereby inherently ensuring coherence. Evaluated on U.S. and French mortality data from 1979 to 2023, the approach demonstrates high predictive accuracy and well-calibrated uncertainty for both aggregate and cause-specific forecasts, supports interpretable demographic pattern analysis, and maintains consistency across sexes and countries.

This study addresses the limitations of traditional mortality models, which assume a fixed discrete structure and thus struggle to capture the age- and time-varying dispersion patterns inherent in real-world data, leading to biased forecasts and poorly calibrated uncertainty. To overcome this, the paper introduces the Conway–Maxwell–Poisson (CMP) distribution into mortality modeling for the first time, establishing a unified framework capable of flexibly representing under-, equi-, and over-dispersion while allowing dispersion levels to vary heterogeneously across age and time dimensions. Employing Bayesian inference with Markov chain Monte Carlo (MCMC) methods, the approach jointly quantifies parameter, process, and distributional uncertainties. Empirical analysis of male mortality data from England and Wales demonstrates that the proposed model substantially improves the calibration of longevity risk and enhances the reliability of annuity pricing.

This study addresses the challenge of effectively reducing and analyzing high-dimensional age-specific mortality probability data, which exhibits complex structural dependencies. The authors propose a time-dependent Beta latent variable model that, for the first time, incorporates an autoregressive prior to capture the temporal evolution of mortality rates. By modeling directly on the original probability scale without requiring a logit transformation, the approach enhances interpretability. Leveraging Bayesian inference with Hamiltonian Monte Carlo sampling, the model accurately reconstructs multi-country, multi-age mortality data using only six latent variables. This performance substantially surpasses that of conventional Gaussian factor analysis, and the inferred latent variables possess clear demographic interpretations.

This study addresses the finite-sample bias of maximum likelihood estimation (MLE) in meta-analyses of rare events, which arises due to data sparsity and studies reporting zero events. To mitigate this issue, the authors propose a maximum penalized likelihood estimation method within the beta-binomial random-effects model by incorporating a penalty term derived from Jeffreys’ prior. They further develop corresponding Wald-type and profile penalized likelihood confidence intervals. The proposed approach substantially enhances estimation stability and inferential reliability in sparse-data settings. Simulation results demonstrate that, particularly when the number of studies is small or event rates are low, the new method outperforms conventional MLE in terms of convergence, bias, and root mean squared error, while its confidence intervals maintain nominal coverage probabilities effectively.

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.