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稳健类贝叶斯估计：Rho-Bayes 估计AI 解读

We observe $n$ independent random variables with joint distribution ${\mathbf{P}}$ and pretend that they are i.i.d. with some common density $s$ (with respect to a known measure $\mu $) that we wish to estimate. We consider a density model $\overline{S}$ for $s$ that we endow with a prior distribution $\pi $ (with support in $\overline{S}$) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$…

模型选择与局部几何AI 解读

We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases—including common classes of causal or graphical models, as well as time series models—distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than…

回归中的经验贝叶斯预言机不确定性量化AI 解读

We propose an empirical Bayes method for high-dimensional linear regression models. Following an oracle approach that quantifies the error locally for each possible value of the parameter, we show that an empirical Bayes posterior contracts at the optimal rate at all parameters and leads to uniform size-optimal credible balls with guaranteed coverage under an “excessive bias restriction” condition. This condition gives rise to a new slicing of the entire space that is…

过度自信的统计检验：矩不等式方法AI 解读

Summary We propose a moment inequality approach to test for the presence of overconfidence using data from ranking experiments where subjects rank themselves relative to other experimental participants. Although a ranking experiment is a typical way to collect data for the analysis of overconfidence, recent studies show that the resulting data may apparently indicate overconfidence even if participants are purely rational Bayesian updaters, in which case a set of…

非可忽略未响应下的贝叶斯标量对图像回归AI 解读

Medical imaging has become an increasingly important tool in screening, diagnosis, prognosis, and treatment of various diseases given its information visualization and quantitative assessment. The aim of this article is to develop a Bayesian scalar-on-image regression model to integrate high-dimensional imaging data and clinical data to predict cognitive, behavioral, or emotional outcomes, while allowing for nonignorable missing outcomes. Such a nonignorable nonresponse…

用于电子健康记录表型识别的贝叶斯双重特征分配AI 解读

Electronic health records (EHR) provide opportunities for deeper understanding of human phenotypes - in our case, latent disease - based on statistical modeling. We propose a categorical matrix factorization method to infer latent diseases from EHR data. A latent disease is defined as an unknown biological aberration that causes a set of common symptoms for a group of patients. The proposed approach is based on a novel double feature allocation model which simultaneously…

面向高维特征预测的定向随机投影AI 解读

Minerva Mukhopadhyaya & David B. Dunsonb Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India Department of Statistical Science, Duke University, Durham, NC Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/JASA. Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA. CONTACT Minerva Mukhopadhyay minervam@iitk.ac.in Department of…

具有共轭满条件分布的自然指数族相关数据贝叶斯层级模型AI 解读

We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called “big n problem.” The computational complexity of the “big n problem” is further exacerbated when allowing for non-Gaussian data models, as is the case here.…

通过期望传播快速准确地分析二元响应混合模型AI 解读

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case…

用于子空间收缩的函数型 Horseshoe 先验AI 解读

We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage acts on the shape of the function rather than inducing sparsity on model parameters. We study the efficacy of the proposed approach by showing an adaptive posterior concentration property on the function. We also demonstrate consistency of…

基因扰动实验的强信号检测：具有功效保证与 FDR 控制的自适应方法AI 解读

The perturbation of a transcription factor should affect the expression levels of its direct targets. However, not all genes showing changes in expression are direct targets. To increase the chance of detecting direct targets, we propose a modified two-group model where the null group corresponds to genes which are not direct targets, but can have small nonzero effects. We model the behavior of genes from the null set by a Gaussian distribution with unknown variance τ 2 . To…

不对可观测数据施加额外限制的灵活观察性研究敏感性分析AI 解读

A fundamental challenge in observational causal inference is that assumptions about unconfoundedness are not testable from data. Assessing sensitivity to such assumptions is therefore important in practice. Unfortunately, some existing sensitivity analysis approaches inadvertently impose restrictions that are at odds with modern causal inference methods, which emphasize flexible models for observed data. To address this issue, we propose a framework that allows (1) flexible…

面向多峰分布的自适应MCMC框架AI 解读

We propose a new Monte Carlo method for sampling from multimodal distributions. The idea of this technique is based on splitting the task into two: finding the modes of a target distribution $\pi$ and sampling, given the knowledge of the locations of the modes. The sampling algorithm relies on steps of two types: local ones, preserving the mode; and jumps to regions associated with different modes. Besides, the method learns the optimal parameters of the algorithm, while it…

贝叶斯结构化线性模型的一般框架AI 解读

High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with a large number of frequentist methodologies, there are rather few theoretically optimal Bayes methods for high dimensional models. This paper provides a unified approach to both Bayes high dimensional statistics and Bayes nonparametrics in a general framework of structured linear models. With a proposed two-step prior, we prove a general oracle…

多元 Hawkes 过程的非参数贝叶斯估计AI 解读

This paper studies nonparametric estimation of parameters of multivariate Hawkes processes. We consider the Bayesian setting and derive posterior concentration rates. First, rates are derived for $\mathbb{L}_{1}$-metrics for stochastic intensities of the Hawkes process. We then deduce rates for the $\mathbb{L}_{1}$-norm of interactions functions of the process. Our results are exemplified by using priors based on piecewise constant functions, with regular or random…

社群识别中均值场变分推断的理论与计算保证AI 解读

The mean field variational Bayes method is becoming increasingly popular in statistics and machine learning. Its iterative coordinate ascent variational inference algorithm has been widely applied to large scale Bayesian inference. See Blei et al. (2017) for a recent comprehensive review. Despite the popularity of the mean field method, there exist remarkably little fundamental theoretical justifications. To the best of our knowledge, the iterative algorithm has never been…

半参数贝叶斯因果推断AI 解读

We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently, we estimate the causal effect of a treatment, correcting nonparametrically for confounding. We show that standard Gaussian process priors satisfy a semiparametric Bernstein–von Mises theorem under smoothness conditions. We further propose a novel propensity score-dependent prior that…

尖峰与厚尾经验贝叶斯多重检验AI 解读

This paper explores a connection between empirical Bayes posterior distributions and false discovery rate (FDR) control. In the Gaussian sequence model this work shows that empirical Bayes-calibrated spike and slab posterior distributions allow a correct FDR control under sparsity. Doing so, it offers a frequentist theoretical validation of empirical Bayes methods in the context of multiple testing. Our theoretical results are illustrated with numerical experiments.

多条计数时间序列的贝叶斯预测AI 解读

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New…

利用贝叶斯 WAND 模型揭示排序数据的子群结构AI 解读

Ranked data arise in many areas of application ranging from the ranking of up-regulated genes for cancer to the ranking of academic statistics journals. Complications can arise when rankers do not report a full ranking of all entities; for example, they might only report their top-M ranked entities after seeing some or all entities. It can also be useful to know whether rankers are equally informative, and whether some entities are effectively judged to be exchangeable.…

资产定价中哪些因子是风险因子？模型扫描框架AI 解读

A key question for understanding the cross-section of expected returns of equities is the following: which factors, from a given collection of factors, are risk factors, equivalently, which factors are in the stochastic discount factor (SDF)? Though the SDF is unobserved, assumptions about which factors (from the available set of factors) are in the SDF restricts the joint distribution of factors in specific ways, as a consequence of the economic theory of asset pricing. A…

无限分解的贝叶斯累积收缩AI 解读

Summary The dimension of the parameter space is typically unknown in a variety of models that rely on factorizations. For example, in factor analysis the number of latent factors is not known and has to be inferred from the data. Although classical shrinkage priors are useful in such contexts, increasing shrinkage priors can provide a more effective approach that progressively penalizes expansions with growing complexity. In this article we propose a novel increasing…

混合模型序贯学习程序的拟贝叶斯性质AI 解读

Summary Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly suboptimal, solutions. The extent to which these algorithms approximate Bayesian solutions is a question of interest, but often unanswered. We propose a methodology to address this question in predictive settings, when the algorithm can be reinterpreted as a probabilistic predictive rule. We specifically…

含随机波动率的大型贝叶斯 VAR 的复合似然方法AI 解读

Summary Adding multivariate stochastic volatility of a flexible form to large vector autoregressions (VARs) involving over 100 variables has proved challenging owing to computational considerations and overparametrization concerns. The existing literature works with either homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility.…