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线性模型的随时有效推断及回归调整因果推断应用AI 解读

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical tests, such as t-tests and F-tests, are only valid at fixed sample sizes, making them unsuitable for sequential settings such as online A/B testing. We develop an anytime-valid theory of inference for the linear model, introducing sequential analogues of classical tests and confidence sets that provide Type-I error control and coverage guarantees…

用于改进估计与推断的贝叶斯迁移学习AI 解读

Transfer learning enhances model performance in a target population with limited samples by leveraging knowledge from related studies. While many works focus on improving predictive performance, challenges persist in statistical inference. Bayesian approaches naturally provide uncertainty quantification for parameter estimates; however, existing Bayesian transfer learning methods are typically limited to single-source scenarios or require individual-level data. We introduce…

基于 Metropolis 调整狄利克雷序列的离散数据非参数预测推断AI 解读

This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (mad) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The…

组合响应数据的统计建模AI 解读

There is a rich literature for modeling binary and polychotomous responses. However, existing methods are inadequate for handling combinatorial responses, where each response is an integer array under additional constraints. Such data are increasingly common in modern applications, such as surveys collected under skip logic, event propagation on a network, and observed matching in ecology. Ignoring the combinatorial structure leads to biased estimation and prediction. The…

采用可扩展子采样的 Metropolis–Hastings 算法AI 解读

The Metropolis–Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement. However, in the context of Bayesian inference for large datasets, evaluating the likelihood on the full data for thousands of iterations until convergence can be prohibitively expensive. This paper introduces a new subsample MH algorithm that…

BAP：多药物多剂量试验的贝叶斯生物标志物辅助平台设计AI 解读

Assessing the long-term benefits of new treatments can be expensive and time-consuming, particularly in disease areas with unmet medical needs. While platform trials enable the evaluation of multiple interventions simultaneously, they currently cannot assess studies involving multiple agents and doses or utilize longitudinal biomarkers in decision-making. We propose a Bayesian biomarker-assisted platform design that offers a unified framework for evaluating multiple…

用于有序回归的延续比Logit结构化混合模型AI 解读

We develop a nonparametric Bayesian modeling approach to ordinal regression based on priors placed directly on the discrete distribution of the ordinal responses. The prior probability models are built from a structured mixture of multinomial distributions. We leverage the continuation-ratio logits representation to formulate the mixture kernel, with mixture weights defined through the logit stick-breaking process that incorporates the covariates through a linear function.…

数据增强算法的快速混合：贝叶斯 probit、logit 与 lasso 回归AI 解读

We propose using a modified conductance-based method to study the mixing time of an important class of two-block Gibbs samplers, the data augmentation (DA) algorithm. Using this method, we prove the first non-asymptotic polynomial upper bounds on mixing times of three important DA algorithms: DA algorithms for Bayesian Probit regression (ProbitDA) and Bayesian Logit regression (LogitDA), and Bayesian Lasso Regression (LassoDA). Concretely, for ProbitDA and LogitDA, we…

使用不精确梯度的无偏动量Langevin Monte CarloAI 解读

We present an unbiased method for Bayesian posterior means based on kinetic Langevin dynamics that combines advanced splitting methods with enhanced gradient approximations. Our approach avoids Metropolis correction by coupling Markov chains at different discretization levels in a multilevel Monte Carlo approach. Theoretical analysis demonstrates that our proposed estimator is unbiased, attains finite variance, and satisfies a central limit theorem. It can achieve accuracy…

污染机制下后验采样的隐私保证AI 解读

In recent years, differential privacy has been adopted by tech-companies and governmental agencies as the standard for measuring privacy in algorithms. In this article, we study differential privacy in Bayesian posterior sampling settings. We begin by considering differential privacy in the most common privatisation setting in which Laplace or Gaussian noise is injected into the output. In an effort to achieve better differential privacy, we consider adopting Huber’s…

因果工具变量模型中的贝叶斯模型平均AI 解读

ABSTRACT Instrumental variables are a popular tool to infer causal effects under unobserved confounding, but choosing suitable instruments is challenging in practice. We propose gIVBMA, a Bayesian model averaging procedure that addresses this challenge by averaging across different sets of instrumental variables and covariates in a structural equation model. This allows for data‐driven selection of valid and relevant instruments and provides additional robustness against…

自回归逆Wishart多元随机波动模型及其因子扩展AI 解读

ABSTRACT Despite its conceptual appeal, the autoregressive inverse‐Wishart (AIW) multivariate stochastic volatility model has been hindered by inefficient sampling methods. The existing samplers for the latent covariance matrix severely suffer from the curse of dimensionality and only work when the dimension is very low. In this paper, we introduce a new proposal for the latent covariance matrix in the AIW model, which demonstrates far better scalability. We introduce…

存在缺失数据时的深度学习AI 解读

Abstract In the context of multivariate nonparametric regression with missing covariates, we propose pattern embedded neural networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural network trained on the imputed data, PENNs pass the vectors of observation indicators through a second neural network to provide a compact representation. The outputs are then combined in a third neural network to produce final…

中介分析中复合原假设的最优检验AI 解读

The indirect effect of an exposure on an outcome through an intermediate variable can be identified by a product of two regression coefficients under certain causal and regression modeling assumptions. In this context, the null hypothesis of no indirect effect is a composite null hypothesis, as the null holds if either regression coefficient is zero. A consequence is that traditional hypothesis tests are severely underpowered near the origin (i.e., when both coefficients are…

通过分而治之实现可扩展的时间序列贝叶斯推断AI 解读

Bayesian computation often scales poorly with increasing data size, motivating developments such as divide-and-conquer approaches for scalable inference. These methods partition the data into subsets, perform parallel inference on each subset, and aggregate the results into a single posterior. Appealing theoretical properties and practical performance have been demonstrated for independent data; however, methods for dependent data remain challenging. Existing methods rely on…

部分识别下的稳健贝叶斯处理选择AI 解读

We study a class of binary treatment choice problems with partial identification through the lens of robust (multiple prior) Bayesian analysis. We use a convenient set of prior distributions to derive ex-ante and ex-post robust Bayes decision rules, both for decision makers who can randomize and for decision makers who cannot. Our main messages are as follows: First, ex-ante and ex-post robust Bayes decision rules do not agree in general, whether or not randomized rules are…

Markov 状态切换扩散的精确贝叶斯推断AI 解读

Abstract We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and volatility. The jumps are driven by a latent, continuous-time Markov switching process. We address the problem through an MCMC and an MCEM algorithm that target the exact posterior of diffusion parameters and the latent regime process.…

分布式差分隐私约束下非参数分类的极小极大与自适应迁移学习AI 解读

Abstract This paper considers minimax and adaptive transfer learning for nonparametric classification under the posterior drift model with distributed differential privacy constraints. Our study is conducted within a heterogeneous framework, encompassing diverse sample sizes, varying privacy parameters, and data heterogeneity across different servers. We first establish the minimax misclassification rate, precisely characterizing the effects of privacy constraints, source…

线性模型选择与预测中的分块 g 先验狄利克雷过程混合AI 解读

This paper introduces Dirichlet process mixtures of block g priors for model selection and prediction in linear models. These priors are extensions of traditional mixtures of g priors that allow for differential shrinkage for various (data-selected) blocks of parameters while fully accounting for the predictors’ correlation structure, providing a bridge between the literatures on model selection and continuous shrinkage priors. We show that Dirichlet process mixtures of…

遗传风险评分构建：投影汇总统计与灵活收缩的稳健贝叶斯方法AI 解读

Polygenic risk scores (PRS) developed from genome-wide association studies (GWAS) can be used for risk stratification by quantifying the genetic contribution to disease, and many clinical applications have been proposed. Bayesian methods are popular for building PRS because of their natural ability to regularize models and incorporate external information. In this article, we present new theoretical results, methods, and extensive numerical studies to advance Bayesian…

多状态状态空间模型的滤波与平滑AI 解读

This paper improves Bayesian filtering techniques in regime-switching state-space models and develops a novel recursion-based smoother for latent variables. The smoother is computationally stable, adaptable to different filters, and easy to implement. We assess its performance in a New Keynesian DSGE model pairing it with three practical filters: the Generalized Pseudo-Bayesian filters of order one (GPB1) and two (GPB2, often referred to as the Kim or Kim–Nelson filter in…

一般度量图上的对数高斯 Cox 过程AI 解读

Abstract The modelling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging Gaussian Whittle–Matérn fields, which are solutions to fractional-order stochastic differential equations on metric graphs. To achieve computationally efficient likelihood-based inference,…

高维多视图数据协方差结构的推断AI 解读

Summary This article focuses on covariance estimation for multi-view data. Popular approaches rely on factor-analytic decompositions with shared and view-specific latent factors. Posterior computation is conducted via expensive and brittle Markov chain Monte Carlo sampling or variational approximations that underestimate uncertainty and lack theoretical guarantees. Our proposed methodology employs spectral decompositions to estimate and align latent factors that are active…

准贝叶斯经验贝叶斯：泊松复合决策问题的序贯方法AI 解读

SUMMARY The Poisson compound decision problem is a long-standing problem is statistics, for which empirical Bayes methods are commonly used to estimate Poisson means in static or batch settings. We consider this problem in a streaming, or online, framework. Building on a quasi-Bayesian approach based on Newton’s algorithm, we develop a sequential estimate that is easy to evaluate, computationally efficient and has constant per-observation cost as the data accrue. We…