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模型选择与不确定性下的内在贝叶斯推断AI 解读

In this article, we present a fully coherent and consistent objective Bayesian analysis of the linear regression model using intrinsic priors. The intrinsic prior is a scaled mixture of g-priors and promotes shrinkage toward the subspace defined by a base (or null) model. While it has been established that the intrinsic prior provides consistent model selectors across a range of models, the posterior distribution of the model parameters has not previously been investigated.…

允许响应与协变量缺失的扩展状态空间模型AI 解读

This article proposes an extended state-space model for accommodating multivariate panel data. The novel aspect of this contribution is an adjustment to the classical model for multiple subjects that allows missingness in the covariates in addition to the responses. Missing covariate data are handled by a second state-space model nested inside the first to represent unobserved exogenous information. Relevant Kalman filter equations are derived, and explicit expressions are…

Dirichlet 过程随机效应模型的估计AI 解读

We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distributions, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of…

二维列联表内禀独立性检验的稳健性评估AI 解读

For testing nested hypotheses from a Bayesian standpoint, a desirable condition is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Furthermore, the degree of concentration of the priors is controlled by a discrete parameter, t, the training sample size, which plays an important role in the resulting answer. In this article we report on…

贝叶斯变量选择程序的一致性AI 解读

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that…

有序贝叶斯社会科学模型的非参数先验：设定与估计AI 解读

A generalized linear mixed model, ordered probit, is used to estimate levels of stress in presidential political appointees as a means of understanding their surprisingly short tenures. A Bayesian approach is developed, where the random effects are modeled with a Dirichlet process mixture prior, allowing for useful incorporation of prior information, but retaining some vagueness in the form of the prior. Applications of Bayesian models in the social sciences are typically…

利用目标函数与随机搜索进行聚类AI 解读

Summary A new approach to clustering multivariate data, based on a multilevel linear mixed model, is proposed. A key feature of the model is that observations from the same cluster are correlated, because they share cluster-specific random effects. The inclusion of cluster-specific random effects allows parsimonious departure from an assumed base model for cluster mean profiles. This departure is captured statistically via the posterior expectation, or best linear unbiased…

客观贝叶斯变量选择AI 解读

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems; that is, they are derived from the model structure and are free from tuning parameters. Thus they can be seen as objective priors for variable…

通过函数型数据预平滑改进相异度估计AI 解读

We examine the effect of presmoothing functional data on estimating the dissimilarities among objects in a dataset, with applications to cluster analysis and other distance methods, such as multidimensional scaling and statistical matching. We prove that a shrinkage method of smoothing results in a better estimator of the dissimilarities among a set of noisy curves. For a model with independent noise structure, the smoothed-data dissimilarity estimator dominates the…

统一区间定位与连锁不平衡定位的一般统计框架AI 解读

The nonrandom association between different genes, termed linkage disequilibrium (LD), provides a powerful tool for high-resolution mapping of quantitative trait loci (QTL) underlying complex traits. This LD-based mapping approach can be made more efficient when it is coupled with interval mapping characterizing the genetic distance between markers and QTL. This article describes a general statistical framework for simultaneously estimating the linkage and LD that are…

回归问题中实用的小样本渐近近似AI 解读

Saddlepoint approximations are derived for sums of independent, but not necessarily identically distributed random variables, along with generalizations to estimating equations and multivariate problems. These results are particularly useful for accurately approximating the distribution of regression coefficients. General formulas are given for the distribution of the coefficients arising out of a generalized linear model with both canonical and noncanonical link functions.…

最优置信集合、生物等效性与帕斯卡蜗线AI 解读

We begin with a decision-theoretic investigation into confidence sets that minimize expected volume at a given parameter value. Such sets are constructed by inverting a family of uniformly most powerful tests, and hence they also enjoy the optimality property of being uniformly most accurate. In addition, these sets possess Bayesian optimal volume properties and represent the first case (to our knowledge) of a frequentist 1 – α confidence set that possesses a Bayesian…

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基于选择性二项信息的估计：如何解读被挑选的击球率AI 解读

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to…

选择性二项信息下的估计：如何理解被挑选的棒球打击率AI 解读

Often sports announcers, particularly in baseball, provide the listener with exaggerated information concerning a player's performance. For example, we may be told that Dave Winfield, a popular baseball player, has hit safely in 8 of his last 17 chances (a batting average of .471). This is biased, or selected information, as the “17” was chosen to maximize the reported percentage. We model this as observing a maximum success rate of a Bernoulli process and show how to…

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提高 Student t 置信区间的置信陈述AI 解读

The usual confidence interval, based on Student's $t$ distribution, has conditional confidence that is larger than the nominal confidence level. Although this fact is known, along with the fact that increased conditional confidence can be used to improve a confidence assertion, the confidence assertion of Student's $t$ interval has never been critically examined. We do so here, and construct a confidence estimator that allows uniformly higher confidence in the interval and…

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正态方差的改进不变置信区间AI 解读

Confidence intervals for the variance of a normal distribution with unknown mean are constructed which improve upon the usual shortest interval based on the sample variance alone. These intervals have guaranteed coverage probability uniformly greater than a predetermined value $1-\alpha$ and have uniformly shorter length. Using information relating the size of the samples mean to that of the sample variance, we smoothly shift the usual minimum length interval closer to zero,…

统计信息与似然：批判性论文集AI 解读

I Information and Likelihood.- I Recovery of Ancillary Information.- 0. Notes.- 1. Introduction.- 2. The Sample Size Analogy.- 3. A Logical Difficulty.- 4. Conceptual Statistical Experiments.- II Statistical Information and Likelihood Part I: Principles.- 0. Notes.- 1. Statistical Information.- 2. Basic Definitions and Relations.- 3. Some Principles of Inference.- 4. Information as a Function.- 5. Fisher Information.- 6. The Likelihood Principle.- III Statistical Information…

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正态方差区间估计量的条件性质AI 解读

Both one-sided and two-sided interval estimators are examined using conditional criteria and we find that most common intervals have acceptable conditional properties. In the two-sided case we further examine three well known intervals and find the shortest-unbiased (Neyman-shortest) interval possessing the strongest conditional properties, with the minimum-length interval a close second. In the one-sided case we have the somewhat surprising result that the lower confidence…

条件可接受的重新定中心集合估计量AI 解读

The usual confidence sphere for a multivariate normal mean can be uniformly improved upon, in terms of coverage probability, by recentering it at a Stein-type estimator. However, these improved sets can have poor conditional performance. Using the theory of relevant betting procedures, which provides an objective means for assessing the conditional performance of a statistical procedure, a criterion for conditional acceptability can be established. A method of constructing…

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