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高斯白噪声模型中的非参数 Bernstein–von Mises 定理AI 解读

Bernstein–von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact $1-\alpha$ frequentist coverage level and whose $L^{2}$-diameter shrinks at the minimax rate of convergence (within logarithmic factors)…

稀疏有向无环图马尔可夫等价类上的可逆MCMCAI 解读

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible…

一致最强贝叶斯检验AI 解读

Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart,…

稳健的 T 最优模型判别设计AI 解读

This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the $T$-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975a) 57–70]. $T$-optimal designs depend on unknown model parameters and it is demonstrated that these designs are sensitive with respect to misspecification. As a solution to this problem we propose a Bayesian and standardized maximin approach to construct…

利用Gibbs抽样输出计算边际数据密度的方法AI 解读

We introduce two estimators for estimating the Marginal Data Density (MDD) from the Gibbs output. Our methods are based on exploiting the analytical tractability condition, which requires that some parameter blocks can be analytically integrated out from the conditional posterior densities. This condition is satisfied by several widely used time series models. An empirical application to six-variate VAR models shows that the bias of a fully computational estimator is…

利用信息性民主先验评估实时VAR预测AI 解读

SUMMARY This paper proposes Bayesian forecasting in a vector autoregression using a democratic prior. This prior is chosen to match the predictions of survey respondents. In particular, the unconditional mean for each series in the vector autoregression is centered around long‐horizon survey forecasts. Heavy shrinkage toward the democratic prior is found to give good real‐time predictions of a range of macroeconomic variables, as these survey projections are good at quickly…

受税率限制的反应函数AI 解读

SUMMARY This paper models for the first time a spatial process in local tax policies in the presence of centrally imposed fiscal limitations. Focusing on the frequently encountered case of a tax rate cap, we evaluate three empirical approaches to the analysis of spatially dependent limited tax policies: (i) a Bayesian spatial approach for censored dependent variables; (ii) a Tobit corner solution model augmented with a spatial lag; (iii) a spatial discrete hazard model. The…

贝叶斯 DSGE 模型的识别问题AI 解读

This article is concerned with local identification of individual parameters of dynamic stochastic general equilibrium (DSGE) models estimated by Bayesian methods. Identification is often judged by a comparison of the posterior distribution of a parameter with its prior. However, these can differ even when the parameter is not identified. Instead, we propose two Bayesian indicators of identification. The first follows a suggestion by Poirier of comparing the posterior…

弱识别动态随机一般均衡模型的频率学派推断AI 解读

A common problem in estimating dynamic stochastic general equilibrium models is that the structural parameters of economic interest are only weakly identified. As a result, classical confidence sets and Bayesian credible sets will not coincide even asymptotically, and the mean, mode, or median of the posterior distribution of the structural parameters can no longer be viewed as a consistent estimator. We propose two methods of constructing confidence intervals for structural…

稀疏向量组的双层稀疏估计AI 解读

We consider estimating a sparse group of sparse normal mean vectors, based on penalized likelihood estimation with complexity penalties on the number of nonzero mean vectors and the numbers of their significant components, which can be performed by a fast algorithm. The resulting estimators are developed within a Bayesian framework and can be viewed as maximum a posteriori estimators. We establish their adaptive minimaxity over a wide range of sparse and dense settings. A…

用相依归一化随机测度混合模型比较分布AI 解读

Summary A methodology for the simultaneous Bayesian non-parametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced…

大规模多重检验的扩展似然方法AI 解读

Summary To date, only frequentist, Bayesian and empirical Bayes approaches have been studied for the large-scale inference problem of testing simultaneously hundreds or thousands of hypotheses. Their derivations start with some summarizing statistics without modelling the basic responses. As a consequence testing procedures have been developed without necessarily checking model assumptions, and empirical null distributions are needed to avoid the problem of rejecting all…

高维惩罚似然中的调节参数选择AI 解读

Summary Determining how to select the tuning parameter appropriately is essential in penalized likelihood methods for high dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear models, where the dimensionality of covariates p is allowed to increase exponentially with the sample size n. We propose to select the tuning parameter by optimizing the generalized information criterion with an appropriate model…

基于条件数正则化的协方差估计AI 解读

Summary Estimation of high dimensional covariance matrices is known to be a difficult problem, has many applications and is of current interest to the larger statistics community. In many applications including the so-called ‘large p, small n’ setting, the estimate of the covariance matrix is required to be not only invertible but also well conditioned. Although many regularization schemes attempt to do this, none of them address the ill conditioning problem directly. We…

SMC²：状态空间模型序贯分析的高效算法AI 解读

Summary We consider the generic problem of performing sequential Bayesian inference in a state space model with observation process y, state process x and fixed parameter θ. An idealized approach would be to apply the iterated batch importance sampling algorithm of Chopin. This is a sequential Monte Carlo algorithm in the θ-dimension, that samples values of θ, reweights iteratively these values by using the likelihood increments pyt∣y1:t−1,θ and rejuvenates the θ-particles…

元分析中异质性方差的估计AI 解读

Summary Several new estimators of the between-study variability in a heterogeneous random effects meta-analysis model are derived. One is the unbiased statistic which is locally optimal for small values of the parameter. Others are Bayes procedures within a class of quadratic statistics for a diffuse prior with different choices of the prior mean. These estimators are compared with the DerSimonian–Laird procedure and the Hedges statistic in particular via the quadratic risk…

潜在位置图上的普遍相合顶点分类AI 解读

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $\kappa$, provided that the latent positions are i.i.d. from some distribution $F$. We then consider the exploitation task of vertex classification where the link function $\kappa$ belongs to the class of universal kernels and class labels are observed for a number of vertices tending to…

高维广义线性模型的贝叶斯子集建模AI 解读

This article presents a new prior setting for high-dimensional generalized linear models, which leads to a Bayesian subset regression (BSR) with the maximum a posteriori model approximately equivalent to the minimum extended Bayesian information criterion model. The consistency of the resulting posterior is established under mild conditions. Further, a variable screening procedure is proposed based on the marginal inclusion probability, which shares the same properties of…

多文件记录链接的广义Fellegi–Sunter框架及凶杀记录应用AI 解读

We present a probabilistic method for linking multiple datafiles. This task is not trivial in the absence of unique identifiers for the individuals recorded. This is a common scenario when linking census data to coverage measurement surveys for census coverage evaluation, and in general when multiple record systems need to be integrated for posterior analysis. Our method generalizes the Fellegi–Sunter theory for linking records from two datafiles and its modern…

墨西哥无尾蝙蝠鸣声音节：非平稳声学时间序列的贝叶斯函数混合模型AI 解读

We describe a new approach to analyze chirp syllables of free-tailed bats from two regions of Texas in which they are predominant: Austin and College Station. Our goal is to characterize any systematic regional differences in the mating chirps and assess whether individual bats have signature chirps. The data are analyzed by modeling spectrograms of the chirps as responses in a Bayesian functional mixed model. Given the variable chirp lengths, we compute the spectrograms on…

高维数据中被选参数的经验贝叶斯置信区间AI 解读

Modern statistical problems often involve a large number of populations and hence a large number of parameters that characterize these populations. It is common for scientists to use data to select the most significant populations, such as those with the largest t statistics. The scientific interest often lies in studying and making inferences regarding these parameters, called the selected parameters, corresponding to the selected populations. The current statistical…

贝叶斯层次泊松回归：青少年驾驶运动学事件研究AI 解读

Although there is evidence that teenagers are at a high risk of crashes in the early months after licensure, the driving behavior of these teenagers is not well understood. The Naturalistic Teenage Driving Study (NTDS) is the first U.S. study to document continuous driving performance of newly-licensed teenagers during their first 18 months of licensure. Counts of kinematic events such as the number of rapid accelerations are available for each trip, and their incidence…

混合数据的贝叶斯高斯 Copula 因子模型AI 解读

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the…

进入医药子市场：贝叶斯面板Probit分析AI 解读

SUMMARY We study entry into pharmaceutical submarkets by using a dynamic panel probit model. We develop a Bayesian version of Wooldridge's approach to dealing with unobserved heterogeneity. We distinguish between greenfield entry (entry with first product) and undifferentiated entry, which may take the form of introducing further products. We extend the standard reduced form model to consider company size in the submarket and across all submarkets. We find that greenfield…