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高维线性回归的经验贝叶斯方法：矩估计与次线性样本复杂度AI 解读

We study empirical Bayes estimation of the prior in high-dimensional linear regression $\mathbf{y}=\mathbf{X}\mathbfβ+\mathbf{\varepsilon}$, where the regression coefficients are drawn independently from an unknown sub-Gaussian prior. In contrast to the sequence model, the design matrix couples the latent coefficients, so that recovering the prior requires deconvolving it from both the noise and copies of itself. We introduce the \emph{Empirical Bayes Method of Moments}…

NP-LEAP：借用历史数据的非参数潜在可交换性先验AI 解读

Bayesian dynamic borrowing (BDB) methods leverage historical data to reduce treatment effect uncertainty, yet existing approaches rely on parametric outcome models susceptible to misspecification. We propose the nonparametric latent exchangeability prior (NP-LEAP), an outcome-agnostic, assumption-lean framework to borrow information from historical data. The NP-LEAP performs individual-level exchangeability assessment, inducing Bayesian model averaging over all possible…

存在处理不依从与多个中介时零膨胀纵向数据的因果中介分析AI 解读

Understanding whether a digital marketing campaign is effective is central to designing effective customer engagement strategies. We analyze a large-scale, longitudinal promotional email campaign conducted by a U.S.\ retailer to evaluate how value-added incentives, such as free shipping, compare with traditional price discounts in influencing customer purchasing behavior. The analysis is complicated by non-compliance, due to not opening emails, multiple longitudinal…

大型贝叶斯张量自回归AI 解读

The availability of multidimensional economic datasets has grown significantly in recent years. An example is bilateral trade values across goods among countries, comprising three dimensions -- importing countries, exporting countries, and goods -- forming a third-order tensor time series. This paper introduces a general Bayesian tensor autoregressive framework to analyze the dynamics of large, multidimensional time series with a particular focus on international trade…

短与超短时间序列的聚类局部投影：分层贝叶斯框架AI 解读

Estimating the dynamic effects of economic shocks in short and very short samples is impeded by a lack of degrees of freedom. We offer a solution based on a Bayesian hierarchical framework for estimating local projection (LP) impulse response functions across a panel of related time series. The framework explicitly accommodates unbalanced panels in which some series are substantially shorter than others, allowing the short series to borrow information from longer ones at…

依赖数据下的 WAIC：线性时间复杂度的协方差修正框架AI 解读

The Widely Applicable Information Criterion (WAIC) is a cornerstone of Bayesian model selection, but its conditional independence assumption renders it inappropriate for sequential and spatially correlated data - a limitation that leads to systematically underestimated model complexity and over-optimistic predictive assessments. We introduce CC-WAIC, a principled generalization of WAIC that explicitly incorporates the full posterior covariance structure of log-likelihood…

宏观审慎政策与下行风险：资本监管的状态依赖效应AI 解读

This paper employs a Threshold Bayesian Vector Autoregression (TBVAR) to estimate the regime-dependent macroeconomic effects of capital regulation in Hungary. Using the Factor-based Index of Systemic Stress (FISS) as the threshold variable, the model identifies normal and stress regimes consistent with the occasionally binding constraints literature. The TBVAR offers a practical multivariate alternative to Growth-at-Risk for data-constrained economies. Generalised impulse…

基于非线性 Wasserstein 投影的贝叶斯分布稳健 Merton 问题AI 解读

We revisit Merton's continuous-time portfolio selection through a data-driven, distributionally robust lens. Our aim is to tap the benefits of frequent trading over short horizons while acknowledging that drift is hard to pin down, whereas volatility can be screened using realized or implied measures for appropriately selected assets. Rather than time-rectangular distributional robust control -- which replenishes adversarial power at every instant and induces over-pessimism…

函数型时间序列结构畸变的检测AI 解读

In the era of modern data science, the rapid proliferation of high-dimensional and functional datasets has fostered increasing interest in the investigation of paradigm shifts and structural breaks. Unlike classical univariate time series, structural changes in functional data need not occur simultaneously across the entire domain; instead, they may emerge locally, producing heterogeneous distortions across the underlying functional structure. The patterns of instability…

广义贝叶斯政策学习AI 解读

This study proposes a General Bayes framework for policy learning. We consider decision problems in which a decision-maker chooses an action from a given set to maximize expected welfare. Typical examples include treatment choice and portfolio optimization. In such problems, the statistical target is a decision rule, and predicting each potential outcome is not necessarily of primary interest. We formulate this policy-learning problem through loss-based Bayesian updating.…

方法选择如何改变统计推断：HIV试验中基线两阶段法与贝叶斯纵向—生存联合模型的比较AI 解读

The two-stage approach and Bayesian joint modeling are commonly used to analyze longitudinal biomarker measurements together with time-to-event outcomes. Using data from an HIV clinical trial of 467 patients with repeated CD4 measurements and all-cause mortality as the survival outcome, we compared a baseline two-stage approach with a Bayesian joint model. The two-stage analysis fitted a linear mixed-effects model and included each patient's predicted baseline CD4 value as a…

时变多重季节性 ARMA 模型AI 解读

We propose an ARMA model that allows for multiple seasonal periods and time varying parameters in both regular and seasonal components, building upon previous work for pure AR processes and the conditional likelihood. The model is parameterized to ensure stability and invertibility at each time point. The parameter evolution is governed by dynamic shrinkage processes, enabling extended periods of essentially constant parameters, gradual changes, and abrupt shifts. The model…

高维线性回归中低维目标参数推断的变分贝叶斯方法AI 解读

We propose a scalable variational Bayes method for statistical inference for a single or pre-specified low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field approximation to the nuisance coordinates and carefully modelling the conditional distribution of the target given the nuisance. This requires only a preprocessing step and preserves the computational advantages of mean-field…

面向预测的推断：对偶与误差AI 解读

Predictively oriented (PrO) inference quantifies uncertainty by selecting a distribution over model parameters to optimize a scoring rule applied to the induced predictive distribution, together with a divergence penalty from a reference distribution. By applying the scoring rule after averaging model densities, PrO inference targets predictive performance, accounting for model misspecification. We focus on the logarithmic score with general $φ$-divergence regularization.…

刻画非对称选择反应的多项 Probit 模型AI 解读

Standard multinomial probit (MNP) models specify symmetric latent utility distributions, implying that choice probabilities respond symmetrically to positive and negative covariate shifts of the same magnitude. This restriction is often implausible in empirical choice settings and can lead to misleading elasticity and substitution predictions. We propose a skewed multinomial probit (SMNP) model that captures asymmetric choice responses by specifying a multivariate…

计数型中间变量的主分层与 BART：生育对女性就业的效应AI 解读

Estimating the causal effect of fertility on women's employment is challenging because fertility and labour-market decisions are jointly determined. Instrumental-variable strategies are widely used, but credible instruments are rare and their validity often depends on covariates. Two-stage least squares, the dominant implementation, does not flexibly accommodate covariate-dependent instrument validity and is poorly suited to count-valued treatment and effect heterogeneity…

尖峰与厚尾先验高维线性回归的 Rényi α 散度变分贝叶斯方法AI 解读

Sparse high-dimensional linear regression is a central problem in statistics, where the goal is often variable selection and/or coefficient estimation. We propose a mean-field variational Bayes approximation for sparse regression with spike-and-slab Laplace priors that replaces the standard Kullback-Leibler (KL) divergence objective with the Rényi's $α$ divergence: a one-parameter generalization of KL divergence indexed by $α\in (0, \infty) \setminus \{1\}$ that allows…

拟可测空间：概率论的一种便利基础AI 解读

We introduce the categories of quasi-measurable spaces, mild generalizations of quasi-Borel spaces that allow for general sample spaces and less restrictive random variables. Each such category is complete, cocomplete, cartesian closed and, as we show, even locally cartesian closed, a quasitopos and a Heyting category, and so models an extensional dependent type theory with a typed intuitionistic first-order logic. We put one probability monad in the foreground, the…

贝叶斯 Dirichlet ARMA 的中心化创新：理论等价与银行资产份额应用AI 解读

We study a minimal change to an observation-driven Bayesian Dirichlet ARMA (B--DARMA) for compositional time series: replace the raw additive log-ratio (ALR) residual in the moving-average block with a centered innovation that subtracts the Dirichlet conditional ALR mean, available in closed form via digamma identities. We prove a recursion-level first-order equivalence (in $1/φ$) between the centered specification and a digamma-link DARMA at fixed parameters, under explicit…

交错双重差分中的部分同质性AI 解读

In staggered difference-in-differences (DiD) designs, units enter treatment at different calendar times, so the treatment effect is not a single number but a set of Cohort-Average Treatment effects on the Treated (CATTs), one per cohort-time cell. Estimating every CATT as its own parameter, as the standard fully flexible estimator does, is unbiased but inefficient when some of these effects are in fact equal, whereas pooling them all into a single two-way fixed effects…

借助多项式逼近建立高斯经验贝叶斯的尖锐遗憾界AI 解读

A central problem in the theory of empirical Bayes is to control the regret (excess risk) of a learned Bayes rule by the Hellinger distance between the estimated and true marginal densities. In the normal means model, the classical result of Jiang and Zhang (2009) achieves this only after regularizing the Bayes rule and incurs an extraneous cubic logarithmic factor through a delicate recursive argument. This paper introduces a new technique, based on polynomial approximation…

带节点乘性效应的网络潜在空间模型AI 解读

Latent space models represent network nodes as points in a geometric space, with connection probabilities determined by distances between latent positions under a fixed metric, typically Euclidean, spherical, or hyperbolic. We generalize the classical formulation by introducing nodal multiplicative effects motivated by a local deformation of the latent metric. This modification approximates a conformal deformation of the metric tensor while preserving the logistic predictor…

高维混合模型的贝叶斯蒸馏聚类AI 解读

Latent subgroup analysis is central to fields such as genomics, precision medicine, and social science, where the goal is to identify heterogeneous populations with distinct covariate structures or response behaviors. Mixture models provide a natural probabilistic framework for this task, representing the data-generating distribution as a weighted combination of subgroup-specific laws with unobserved labels. In high-dimensional regimes, these analyses face significant…

可扩展的 VARMA 模型估计AI 解读

Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization…