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序贯 Gibbs 后验及其主成分分析应用AI 解读

Summary Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter that weights the information in the loss relative to the prior and provides control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference; however, in many situations, the inclusion of a single tuning parameter inevitably leads to poor uncertainty quantification. In particular,…

一类参数化鞅后验的渐近理论AI 解读

Summary The martingale posterior framework replaces the elicitation of the likelihood and prior with that of a sequence of one-step-ahead predictive densities for Bayesian inference. Posterior sampling then involves the imputation of unobserved quantities and can then be carried out in an expedient and parallelizable manner using predictive resampling, without requiring Markov chain Monte Carlo. Recent work has investigated the use of plug-in parametric predictive densities,…

黎曼流形上的测地线切片采样AI 解读

Summary We propose a theoretically justified and practically applicable slice-sampling-based Markov chain Monte Carlo method for approximate sampling from probability measures on Riemannian manifolds. The latter naturally arise as posterior distributions in Bayesian inference of matrix-valued parameters, for example belonging to either the Stiefel or the Grassmann manifold. Our method, called geodesic slice sampling, generalizes hit-and-run slice sampling on $ \mathbb{R}^{d} $…

非线性遗憾下的处理选择AI 解读

Summary Following Savage (1951)and Manski (2004), the literature on statistical treatment choice focuses on the mean of welfare regret. Ignoring other features of the regret distribution, however, can lead to a rule that is sensitive to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean-square regret, we derive closed-form fractions for…

流形数据的经验似然AI 解读

Abstract There has been growing interest in statistical analysis of random objects taking values in a non-Euclidean metric space. One important class of such objects consists of data on manifolds. This article is concerned with inference on the Fréchet mean and related population objects on manifolds. We develop the concept of nonparametric likelihood for data on manifolds and propose general inference methods by adapting the theory of empirical likelihood. In addition to…

Wicksell 问题中经保序化后验的半参数 Bernstein–von Mises 现象AI 解读

In this paper, we propose a novel Bayesian approach for nonparametric estimation in Wicksell’s problem. This has important applications in astronomy for estimating the distribution of the positions of the stars in a galaxy given projected stellar positions and in materials science to determine the 3D microstructure of a material, using its 2D cross-sections. We deviate from the classical Bayesian nonparametric approach, which would place a Dirichlet Process (DP) prior on the…

泊松经验贝叶斯估计：何时先验建模优于边际建模？AI 解读

Empirical Bayes (EB) is a popular framework for large-scale inference that aims to find data-driven estimators to compete with the Bayesian oracle that knows the true prior. Two principled approaches to EB estimation have emerged over the years: f-modeling, which constructs an approximate Bayes rule by estimating the marginal distribution of the data, and g-modeling, which estimates the prior from data and then applies the learned Bayes rule. For the Poisson model, the…

可能性推断模型：综述AI 解读

An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher’s fiducial argument have similar objectives, but a fundamental distinction between the two is that the former doesn’t require that uncertainty quantification be probabilistic, offering greater flexibility and allowing for a proof of its reliability. Important recent developments have been made…

通过测度分解实现稀疏线性回归的高效后验采样AI 解读

We consider the problem of sampling from the posterior distribution of a d-dimensional coefficient vector θ, given linear observations y=Xθ+ε. For sparse Bayesian models, such posteriors are in general multimodal, and therefore challenging to sample from. This observation has prompted the exploration of various heuristics that aim at approximating the posterior distribution. In this article, we study a different approach based on decomposing the posterior distribution into a…

ERP 脑机接口迁移学习中的贝叶斯信号匹配AI 解读

An Event-Related Potential (ERP)-based Brain-Computer Interface (BCI) Speller System assists people with disabilities to communicate by decoding electroencephalogram (EEG) signals. A P300-ERP embedded in EEG signals arises in response to a rare, but relevant event (target) among a series of irrelevant events (non-target). Different machine learning methods have constructed binary classifiers to detect target events, known as calibration. The existing calibration strategy…

整群随机试验中多重中介与溢出效应的贝叶斯非参数方法AI 解读

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…

加性多指标高斯过程及其在夸克—胶子等离子体多物理代理建模中的应用AI 解读

The Quark-Gluon Plasma (QGP) is a unique phase of nuclear matter, theorized to have filled the Universe shortly after the Big Bang. A critical challenge in studying the QGP is that, to reconcile experimental observables with theoretical parameters, one requires many simulation runs of a complex physics model over a high-dimensional parameter space. Each run is computationally expensive, requiring thousands of CPU hours, thus limiting physicists to only several hundred runs.…

结合控制函数的准贝叶斯估计与推断AI 解读

This paper introduces a quasi-Bayesian method that integrates frequentist nonparametric estimation with Bayesian inference in a two-stage process. Applied to an endogenous discrete choice model, the approach first uses kernel or sieve estimators to estimate the control function nonparametrically, followed by Bayesian methods to estimate the structural parameters. This combination leverages the advantages of both frequentist tractability for nonparametric estimation and…

局部稳健且半参数有效的贝叶斯推断AI 解读

We propose a framework for making Bayesian parametric models robust to local misspecification. Suppose in a baseline parametric model, a parameter of interest has an interpretation in an encompassing semiparametric model. Bayesian and maximum likelihood estimators are generally biased under local misspecification. We propose to augment the baseline likelihood by a multiplicative factor that involves scores for the baseline model, the efficient scores for the encompassing…

通过近似后验传达科学不确定性AI 解读

We cast the problem of communicating scientific uncertainty as one of reporting a posterior distribution on an unknown parameter to an audience of Bayesian decision‐makers. We establish novel bounds on the audience's regret when the analyst reports an approximation to a posterior that the audience treats as exact. Under a palatable restriction on the audience's decision problems, the bounds take an especially convenient form. Under a further restriction on the audience's…

估计精度能够预测参数时的经验贝叶斯方法AI 解读

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable and empirically rejected. This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parameterized location‐scale family of distributions, leading to a family of methods that we call…

面板数据预测：估计不确定性与参数异质性AI 解读

We provide a comprehensive examination of the predictive accuracy of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter…

非参数隐马尔可夫与独立同分布模型中的聚类风险AI 解读

We conduct an in-depth analysis of the Bayes risk of clustering in the context of hidden Markov and i.i.d. models. In both settings, we identify the situations where this risk is comparable to the Bayes risk of classification and those where its minimizer, the Bayes clusterer, can be derived from the Bayes classifier. While we demonstrate that clustering based on the Bayes classifier does not always match the optimal Bayes clusterer, we show that this difference is primarily…

通过边际处理效应进行福利分析AI 解读

We consider a causal structure with endogeneity, i.e., unobserved confoundedness, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization rules. Focusing…

部分放宽正交区组结构下混合水平多层析因设计的正交化矩偏差AI 解读

Abstract Multi-stratum factorial designs, such as block designs and row–column designs, are widely used for screening treatment factors in experiments involving complex structures of experimental units due to multiple sources of error. In this study, we propose a unified model-free approach, termed orthogonalized moment aberration, to compare the similarities between level combinations of treatment factors assigned to heterogeneous experimental units. The proposed approach,…

具有排斥与吸引原子的贝叶斯混合模型AI 解读

Abstract The study of almost surely discrete random probability measures is an active line of research in Bayesian non-parametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant interest in the context of Bayesian mixture models. This allows the definition of priors that encourage well-separated and interpretable clusters. In this work, we provide a unified framework for the construction and the Bayesian…

用于贝叶斯多视图聚类的乘积中心狄利克雷过程AI 解读

Abstract While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions…

二阶无偏贝叶斯估计量的先验构造AI 解读

Summary Asymptotically unbiased priors, introduced by Hartigan (1965), are designed to achieve second-order unbiasedness of Bayes estimators. This paper extends Hartigan’s framework to non-independent-and-identically-distributed models by deriving a system of partial differential equations that characterizes asymptotically unbiased priors. Furthermore, we establish a necessary and sufficient condition for the existence of such priors and propose a simple procedure for…

多元高斯累积分布函数与对偶贝叶斯 probit 模型的边际似然AI 解读

Summary The computation of multivariate Gaussian cumulative distribution functions is a key step in many statistical procedures, often representing a crucial computational bottleneck. Over the past few decades, efficient algorithms have been proposed to address this problem, mainly using Monte Carlo solutions. This work highlights a connection between the multivariate Gaussian cumulative distribution function and the marginal likelihood of a tailored dual Bayesian probit…