arXiv subjects

Yuki Ohnishi

Publications and source records attributed to Yuki Ohnishi.

14 recordsLinked to original sources

arXiv2026

Calibrated Bayes analysis of cluster-randomized trials

In cluster-randomized trials (CRTs), entire clusters of individuals are randomized to treatment, and outcomes within a cluster are typically correlated. While frequentist approaches are standard practice for CRT analysis, Bayesian methods have emerged as a strong alternative. Previous work has investigated the use of Bayesian hierarchical models for continuous, binary, and count outcomes in CRTs, but these approaches focus on model-based treatment effect coefficients as the target estimands, which may have ambiguous interpretation under model misspecification and informative cluster size. In this article, we introduce a calibrated Bayesian procedure for estimand-aligned analysis of CRTs even in the presence of potentially misspecified models. We propose estimators targeting both the cluster-average treatment effect (cluster-ATE) and individual-average treatment effect (individual-ATE), particularly in scenarios with informative cluster sizes. We additionally explore strategies for summarizing the posterior samples that can achieve the frequentist coverage even under working model misspecification. We provide simulation evidence to demonstrate the model-robustness property of the proposed estimators in CRTs, and further investigate the impact of covariate adjustment as well as the use of more flexible Bayesian nonparametric working models in the CRT context.

stat.ME↗

arXiv2026

Bayesian change-plane regression

Change-plane regression represents treatment effect heterogeneity through an interpretable rule that assigns patients to two groups according to whether a linear score of baseline covariates crosses a threshold. Although easy to communicate, likelihood-based inference for the hard threshold is nonregular, invalidating standard large-sample approximations. We develop a Bayesian framework that replaces the sharp indicator with a smooth probit gate at a declared smoothing scale and treats the smoothed subgroup rule as the reported estimand. At a fixed smoothing scale, the posterior satisfies a misspecified Bernstein--von Mises theorem centered at the smoothed rule. Under a vanishing smoothing schedule, the posterior learns the boundary faster than the parametric rate, while within an explicit schedule window the regression block and treatment-effect contrast satisfy a Bernstein--von Mises theorem centered at the hard-threshold values with known-subgroup oracle efficiency. Thus, effect inference pays no first-order price for regularization. A decision-theoretic reporting protocol with consistency guarantees separates evidence of heterogeneity from reporting a boundary. Computation uses latent-variable augmentation, a great-circle elliptical slice sampler, and a normalized horseshoe prior. Simulations and an application to the PREMIER trial illustrate the method.

stat.ME↗

arXiv2026

The Resolution of Causal Heterogeneity

Causal subgroup analyses often report a small number of groups summarizing treatment effect heterogeneity, as if that number were a well-defined estimand. Outside genuinely latent class populations, however, a ``true'' subgroup count is model dependent rather than a population functional. We replace it with a new population estimand, the resolution profile, a functional of the causal feature law giving the fewest groups explaining a prescribed fraction of causal heterogeneity, defined for every population without latent structure. Inference is organized around one cross-fitted Bayesian-bootstrap posterior for a single structured moment process, its scores corrected with influence functions, so that paths, profiles, fixed-resolution summaries, and subgroup effects follow by composition. A uniform conditional Bernstein--von Mises theorem over a loss class containing the nonsmooth quantization losses shows this posterior merges with the efficient Gaussian limit under stated nuisance-rate and margin conditions. Subgroup-number uncertainty is not model selection but threshold nonregularity, the profile being an integer-valued threshold of a continuous path, discontinuous in the law at each knot. At these knots no single-valued selector is locally uniformly consistent over root-$n$ neighborhoods, and the set-valued report obtained by inverting a simultaneous band retains locally uniform validity over exactly the same perturbations. Simulations support the approximations, and an analysis of the MineThatData e-mail experiment illustrates the resolution-indexed report, in which two to three groups summarize the visit response while finer structure falls below a noise-floor diagnostic.

stat.ME↗

arXiv2026

Sensitivity analysis for causal mediation: bridge score, sharp sensitivity bounds, and calibration

Causal mediation analysis decomposes the total treatment effect into a portion operating through a hypothesized mediator and a residual direct portion. Identification of natural direct and indirect effects typically rests on the mediator stage of sequential ignorability, which cannot be empirically verified and requires explicit sensitivity analysis. We formulate the \emph{bridge score}, a mediator-stage balancing score, as a low-dimensional vector formed from the two treatment-specific mediator densities at a common mediator value, and show that it balances baseline covariates for the mediator stage relevant to natural effect identification. Conditional on the bridge score, we derive a sharp pointwise variance envelope on the unidentified mediator-outcome confounding function in terms of latent outcome relevance and residual selection. To make the bound operational for sensitivity analysis, we further introduce a residual budget calibration approach based on local residual outcome variation and record a complementary range bound for support-based restrictions. Finally, we show how the pointwise bound can be operationalized for inference through a scalar functional reduction and a Bayesian g-computation algorithm that combines observed-data posterior uncertainty with user-specified sensitivity uncertainty, rather than treating the unidentified sensitivity corrections as learned from the likelihood.

stat.ME↗

arXiv2026

Identification and estimation of causal mechanisms in cluster-randomized trials with post-treatment confounding using Bayesian nonparametrics

Causal mediation analysis in cluster-randomized trials (CRTs) is essential for explaining how cluster-level interventions affect individual outcomes, yet it is complicated by interference, post-treatment confounding, and hierarchical covariate adjustment. We develop a Bayesian nonparametric framework that simultaneously accommodates interference and a post-treatment confounder that precedes the mediator. Identification is achieved through a multivariate Gaussian copula that replaces cross-world independence with a single dependence parameter, yielding a built-in sensitivity analysis to residual post-treatment confounding. For estimation, we introduce a nested common atoms enriched Dirichlet process (CA-EDP) prior that integrates the Common Atoms Model (CAM) to share information across clusters while capturing between- and within-cluster heterogeneity, and an Enriched Dirichlet Process (EDP) structure delivering robust covariate adjustment without impacting the outcome model. We provide formal theoretical support for our prior by deriving the model's key distributional properties, including its partially exchangeable partition structure, and by establishing convergence guarantees for the practical truncation-based posterior inference strategy. We demonstrate the performance of the proposed methods in simulations and provide further illustration through a reanalysis of a completed CRT.

stat.ME↗

arXiv2026

Principal stratification with recurrent events truncated by a terminal event: A nested Bayesian nonparametric approach

Recurrent events often serve as key endpoints in clinical studies but may be prematurely truncated by terminal events such as death, creating selection bias and complicating causal inference. To address this challenge, we develop a Bayesian nonparametric framework to address potential selection bias due to truncation by death within the continuous-time principal stratification framework. We introduce causal estimands for recurrent events in the presence of a terminal event and derive a partial identification result for the estimand under a dual-frailty framework, enabling transparent sensitivity analysis for non-identifiable parameters. We then propose a flexible Bayesian nonparametric prior, the enriched dependent Dirichlet process, specifically designed for joint modeling of recurrent and terminal events, addressing a limitation where standard Dirichlet process priors create random partitions dominated by recurrent events, yielding poor predictive performance for terminal events. Simulations are carried out to show that our method has superior performance compared to existing methods. We apply the proposed new Bayesian nonparametric methods to infer the causal effect of a structured exercise program on rehospitalizations, which are subject to truncation by death.

stat.ME↗

arXiv2025

Differentially Private Covariate Balancing Causal Inference

Differential privacy is the leading mathematical framework for privacy protection, providing a probabilistic guarantee that safeguards individuals' private information when publishing statistics from a dataset. This guarantee is achieved by applying a randomized algorithm to the original data, which introduces unique challenges in data analysis by distorting inherent patterns. In particular, causal inference using observational data in privacy-sensitive contexts is challenging because it requires covariate balance between treatment groups, yet checking the true covariates is prohibited to prevent leakage of sensitive information. In this article, we present a differentially private two-stage covariate balancing weighting estimator to infer causal effects from observational data. Our algorithm produces both point and interval estimators with statistical guarantees, such as consistency and rate optimality, under a given privacy budget.

stat.ME↗

arXiv2025

Degree of Interference: A General Framework For Causal Inference Under Interference

One core assumption typically adopted for valid causal inference is that of no interference between experimental units, i.e., the outcome of an experimental unit is unaffected by the treatments assigned to other experimental units. This assumption can be violated in real-life experiments, which significantly complicates the task of causal inference. As the number of potential outcomes increases, it becomes challenging to disentangle direct treatment effects from ``spillover'' effects. Current methodologies are lacking, as they cannot handle arbitrary, unknown interference structures to permit inference on causal estimands. We present a general framework to address the limitations of existing approaches. Our framework is based on the new concept of the ``degree of interference'' (DoI). The DoI is a unit-level latent variable that captures the latent structure of interference. We also develop a data augmentation algorithm that adopts a blocked Gibbs sampler and Bayesian nonparametric methodology to perform inferences on the estimands under our framework. We illustrate the DoI concept and properties of our Bayesian methodology via extensive simulation studies and an analysis of a randomized experiment investigating the impact of a cash transfer program for which interference is a critical concern. Ultimately, our framework enables us to infer causal effects without strong structural assumptions on interference.

stat.ME↗

arXiv2025

A Bayesian nonparametric approach to mediation and spillover effects with multiple mediators in cluster-randomized trials

Cluster randomized trials (CRTs) with multiple unstructured mediators present significant methodological challenges for causal inference due to within-cluster correlation, interference among units, and the complexity introduced by multiple mediators. Existing causal mediation methods often fall short in simultaneously addressing these complexities, particularly in disentangling mediator-specific effects under interference that are central to studying complex mechanisms. To address this gap, we propose new causal estimands for spillover mediation effects that differentiate the roles of each individual's own mediator and the spillover effects resulting from interactions among individuals within the same cluster. We establish identification results for each estimand and, to flexibly model the complex data structures inherent in CRTs, we develop a new Bayesian nonparametric prior -- the Nested Dependent Dirichlet Process Mixture -- designed for flexibly capture the outcome and mediator surfaces at different levels. We conduct extensive simulations across various scenarios to evaluate the frequentist performance of our methods, compare them with a Bayesian parametric counterpart and illustrate our new methods in an analysis of a completed CRT.

stat.ME↗

arXiv2023

Locally Private Causal Inference for Randomized Experiments

Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in additional bias and variance in their analyses. Thus it is of great importance for analysts to incorporate the privacy noise into valid inference. In this article, we develop methodologies to infer causal effects from locally privatized data under randomized experiments. First, we present frequentist estimators under various privacy scenarios with their variance estimators and plug-in confidence intervals. We show a naïve debiased estimator results in inferior mean-squared error (MSE) compared to minimax lower bounds. In contrast, we show that using a customized privacy mechanism, we can match the lower bound, giving minimax optimal inference. We also develop a Bayesian nonparametric methodology along with a blocked Gibbs sampling algorithm, which can be applied to any of our proposed privacy mechanisms, and which performs especially well in terms of MSE for tight privacy budgets. Finally, we present simulation studies to evaluate the performance of our proposed frequentist and Bayesian methodologies for various privacy budgets, resulting in useful suggestions for performing causal inference for privatized data.

stat.ME↗

arXiv2023

A Bayesian Analysis of Two-Stage Randomized Experiments in the Presence of Interference, Treatment Nonadherence, and Missing Outcomes

Three critical issues for causal inference that often occur in modern, complicated experiments are interference, treatment nonadherence, and missing outcomes. A great deal of research efforts has been dedicated to developing causal inferential methodologies that address these issues separately. However, methodologies that can address these issues simultaneously are lacking. We propose a Bayesian causal inference methodology to address this gap. Our methodology extends existing causal frameworks and methods, specifically, two-staged randomized experiments and the principal stratification framework. In contrast to existing methods that invoke strong structural assumptions to identify principal causal effects, our Bayesian approach uses flexible distributional models that can accommodate the complexities of interference and missing outcomes, and that ensure that principal causal effects are weakly identifiable. We illustrate our methodology via simulation studies and a re-analysis of real-life data from an evaluation of India's National Health Insurance Program. Our methodology enables us to identify new active causal effects that were not identified in past analyses. Ultimately, our simulation studies and case study demonstrate how our methodology can yield more informative analyses in modern experiments with interference, treatment nonadherence, missing outcomes, and complicated outcome generation mechanisms.

stat.ME↗

arXiv2022

Applying Bayesian Hierarchical Probit Model to Interview Grade Evaluation

Job interviews are a fundamental activity for most corporations to acquire potential candidates, and for job seekers to get well-rewarded and fulfilling career opportunities. In many cases, interviews are conducted in multiple processes such as telephone interviews and several face-to-face interviews. At each stage, candidates are evaluated in various aspects. Among them, grade evaluation, such as a rating on a 1-4 scale, might be used as a reasonable method to evaluate candidates. However, because each evaluation is based on a subjective judgment of interviewers, the aggregated evaluations can be biased because the difference in toughness of interviewers is not examined. Additionally, it is noteworthy that the toughness of interviewers might vary depending on the interview round. As described herein, we propose an analytical framework of simultaneous estimation for both the true potential of candidates and toughness of interviewers' judgment considering job interview rounds, with algorithms to extract unseen knowledge of the true potential of candidates and toughness of interviewers as latent variables through analyzing grade data of job interviews. We apply a Bayesian Hierarchical Ordered Probit Model to the grade data from HRMOS, a cloud-based Applicant Tracking System (ATS) operated by BizReach, Inc., an IT start-up particularly addressing human-resource needs in Japan. Our model successfully quantifies the candidate potential and the interviewers' toughness. An interpretation and applications of the model are given along with a discussion of its place within hiring processes in real-world settings. The parameters are estimated by Markov Chain Monte Carlo (MCMC). A discussion of uncertainty, which is given by the posterior distribution of the parameters, is also provided along with the analysis.

stat.AP↗

arXiv2020

Novel Change of Measure Inequalities with Applications to PAC-Bayesian Bounds and Monte Carlo Estimation

We introduce several novel change of measure inequalities for two families of divergences: $f$-divergences and $α$-divergences. We show how the variational representation for $f$-divergences leads to novel change of measure inequalities. We also present a multiplicative change of measure inequality for $α$-divergences and a generalized version of Hammersley-Chapman-Robbins inequality. Finally, we present several applications of our change of measure inequalities, including PAC-Bayesian bounds for various classes of losses and non-asymptotic intervals for Monte Carlo estimates.

cs.LG↗

arXiv2020

Bayesian Hierarchical Bernoulli-Weibull Mixture Model for Extremely Rare Events

Estimating the duration of user behavior is a central concern for most internet companies. Survival analysis is a promising method for analyzing the expected duration of events and usually assumes the same survival function for all subjects and the event will occur in the long run. However, such assumptions are inappropriate when the users behave differently or some events never occur for some users, i.e., the conversion period on web services of the light users with no intention of behaving actively on the service. Especially, if the proportion of inactive users is high, this assumption can lead to undesirable results. To address these challenges, this paper proposes a mixture model that separately addresses active and inactive individuals with a latent variable. First, we define this specific problem setting and show the limitations of conventional survival analysis in addressing this problem. We demonstrate how naturally our Bernoulli-Weibull model can accommodate the challenge. The proposed model was extended further to a Bayesian hierarchical model to incorporate each subject's parameter, offering substantial improvements over conventional, non-hierarchical models in terms of WAIC and WBIC. Second, an experiment and extensive analysis were conducted using real-world data from the Japanese job search website, CareerTrek, offered by BizReach, Inc. In the analysis, some research questions are raised, such as the difference in activation rate and conversion rate between user categories, and how instantaneously the rate of event occurrence changes as time passes. Quantitative answers and interpretations are assigned to them. Furthermore, the model is inferred in a Bayesian manner, which enables us to represent the uncertainty with a credible interval of the parameters and predictive quantities.

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