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处理不完整依从信息的贝叶斯分层 CACE 模型：硬膜外镇痛与剖宫产的荟萃分析AI 解读

Noncompliance with assigned treatments is a common challenge in analyzing and interpreting randomized clinical trials (RCTs). One way to handle noncompliance is to estimate the complier-average causal effect (CACE), the intervention's efficacy in the subpopulation that complies with assigned treatment. In a two-step meta-analysis, one could first estimate CACE for each study, then combine them to estimate the population-averaged CACE. However, when some trials do not report…

刻画有向脑网络的贝叶斯状态空间方法AI 解读

The human brain is a directional network system of brain regions involving directional connectivity. Seizures are a directional network phenomenon as abnormal neuronal activities start from a seizure onset zone (SOZ) and propagate to otherwise healthy regions. To localize the SOZ of an epileptic patient, clinicians use intracranial electroencephalography (iEEG) to record the patient’s intracranial brain activity in many small regions. iEEG data are high-dimensional…

通过图距离建模网络总体AI 解读

This article introduces a new class of models for multiple networks. The core idea is to parameterize a distribution on labeled graphs in terms of a Fréchet mean graph (which depends on a user-specified choice of metric or graph distance) and a parameter that controls the concentration of this distribution about its mean. Entropy is the natural parameter for such control, varying from a point mass concentrated on the Fréchet mean itself to a uniform distribution over all…

计算机模型的贝叶斯投影校准AI 解读

We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the…

在线性模型中引出、纳入并约束识别信念的框架AI 解读

To estimate causal effects from observational data, an applied researcher must impose beliefs. The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest. Yet beliefs about instrument validity do not exist in isolation. Applied researchers often discuss the likely direction of selection and the potential for measurement error in their articles but lack formal tools for incorporating…

具有门槛边界的门槛回归AI 解读

This article studies computation, estimation, inference, and testing for linearity in threshold regression with a threshold boundary. We first put forward a new algorithm to ease the computation of the threshold boundary, and develop the asymptotics for the least squares estimator in both the fixed-threshold-effect framework and the small-threshold-effect framework. We also show that the inverting-likelihood-ratio method is not suitable to construct confidence sets for the…

延迟接受随机游走 Metropolis 算法的效率AI 解读

Delayed-acceptance Metropolis–Hastings and delayed-acceptance pseudo-marginal Metropolis–Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation thereof, but a computationally cheap deterministic approximation is available. An initial accept–reject stage uses the cheap approximation for computing the Metropolis–Hastings ratio; proposals which are accepted at this stage are subjected to a…

用 Wasserstein 距离度量贝叶斯非参数模型的依赖性AI 解读

The proposal and study of dependent Bayesian nonparametric models has been one of the most active research lines in the last two decades, with random vectors of measures representing a natural and popular tool to define them. Nonetheless, a principled approach to understand and quantify the associated dependence structure is still missing. We devise a general, and not model-specific, framework to achieve this task for random measure based models, which consists in: (a)…

凸约束下选择后推断的整合方法AI 解读

Inference after model selection has been an active research topic in the past few years, with numerous works offering different approaches to addressing the perils of the reuse of data. In particular, major progress has been made recently on large and useful classes of problems by harnessing general theory of hypothesis testing in exponential families, but these methods have their limitations. Perhaps most immediate is the gap between theory and practice: implementing the…

高斯过程回归的变量选择一致性AI 解读

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable selection, are known to also adapt to the unknown intrinsic dimension of a sparse true regression function. But it remains unclear if such extensions offer variable selection consistency, that is, if the true subset of important variables…

混合 Logit 模型的稀疏协方差估计AI 解读

Summary This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of…

用于可扩展模型选择的近似拉普拉斯近似AI 解读

Abstract We propose the approximate Laplace approximation (ALA) to evaluate integrated likelihoods, a bottleneck in Bayesian model selection. The Laplace approximation (LA) is a popular tool that speeds up such computation and equips strong model selection properties. However, when the sample size is large or one considers many models the cost of the required optimizations becomes impractical. ALA reduces the cost to that of solving a least-squares problem for each model.…

空间数据的联合分位数回归AI 解读

Abstract Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency between observation units, largely because such methods are not based upon a fully generative model of the data. For analysing spatially indexed data, we address this difficulty by generalizing the joint quantile regression model…

高阶随机波动率模型的简便估计与推断AI 解读

We study the problem of estimating higher-order stochastic volatility [SV(p)] models. Due to the difficulty of evaluating the likelihood function, this remains a challenging problem, even in the relatively simple SV(1) case. We propose simple moment-based winsorized ARMA-type estimators, which are computationally inexpensive and remarkably accurate. The proposed estimators do not require choosing a sampling algorithm, initial parameter values, or an auxiliary model. We show…

结构变化断点日期的连续记录Laplace推断AI 解读

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2020a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution,…

通过类 Gibbs 步骤实现逐分量近似贝叶斯计算AI 解读

Summary Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are, however, sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this dimension grows. To tackle this difficulty we explore a Gibbs version of the approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior…

查尔斯·斯坦与不变性：从 Hunt–Stein 定理谈起AI 解读

When statistical decision theory was emerging as a promising new paradigm, Charles Stein was to play a major role in the development of minimax theory for invariant statistical problems. In some of his earliest work with Gil Hunt, he set out to prove that, in problems where invariant procedures have constant risk, any best invariant test would be minimax among all tests. Although finding it not quite true in general, this led to the legendary Hunt–Stein theorem, which…

高斯过程建模中参考后验分布的正常性AI 解读

In a seminal article, Berger, De Oliveira and Sansó [J. Amer. Statist. Assoc. 96 (2001) 1361–1374] compare several objective prior distributions for the parameters of Gaussian process models with isotropic correlation kernel. The reference prior distribution stands out among them insofar as it always leads to a proper posterior. They prove this result for rough correlation kernels: Spherical, Exponential with power ρ<2, Matérn with smoothness ν<1. This paper provides a proof…

时间序列中变点的最优估计AI 解读

This paper establishes asymptotic theory for optimal estimation of change points in general time series models under α-mixing conditions. We show that the Bayes-type estimator is asymptotically minimax for change-point estimation under squared error loss. Two bootstrap procedures are developed to construct confidence intervals for the change points. An approximate limiting distribution of the change-point estimator under small change is also derived. Simulations and real…

用于α散度最小化的无限维梯度下降AI 解读

This paper introduces the (α,Γ)-descent, an iterative algorithm which operates on measures and performs α-divergence minimisation in a Bayesian framework. This gradient-based procedure extends the commonly-used variational approximation by adding a prior on the variational parameters in the form of a measure. We prove that for a rich family of functions Γ, this algorithm leads at each step to a systematic decrease in the α-divergence and derive convergence results. Our…

扩展可容许决策程序及其非标准贝叶斯风险AI 解读

For finite parameter spaces, among decision procedures with finite risk functions, a decision procedure is extended admissible if and only if it is Bayes. Various relaxations of this classical equivalence have been established for infinite parameter spaces, but these extensions are each subject to technical conditions that limit their applicability, especially to modern (semi and nonparametric) statistical problems. Using results in mathematical logic and nonstandard…

马尔可夫蒙特卡洛的 Peskun–Tierney 排序：超越可逆情形AI 解读

Historically time-reversibility of the transitions or processes underpinning Markov chain Monte Carlo methods (MCMC) has played a key role in their development, while the self-adjointness of associated operators together with the use of classical functional analysis techniques on Hilbert spaces have led to powerful and practically successful tools to characterise and compare their performance. Similar results for algorithms relying on nonreversible Markov processes are…

度量空间中的普遍贝叶斯一致性AI 解读

We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes consistent in all metric spaces admitting any such learner, making it an “optimistically universal” Bayes-consistent learner. This is the first learning algorithm known to enjoy this property; by comparison, the k-NN classifier and its variants are not generally universally Bayes consistent, except under additional structural…

空间计量模型贝叶斯估计的大样本性质AI 解读

This paper studies asymptotic properties of a posterior probability density and Bayesian estimators of spatial econometric models in the classical statistical framework. We focus on the high-order spatial autoregressive model with spatial autoregressive disturbance terms, due to a computational advantage of Bayesian estimation. We also study the asymptotic properties of Bayesian estimation of the spatial autoregressive Tobit model, as an example of nonlinear spatial models.…