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通过Gibbs采样进行变量选择AI 解读

A crucial problem in building a multiple regression model is the selection of predictors to include. The main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets. This procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices. In this framework the promising subsets of predictors can be identified as those…

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存在干扰参数时后验分位数的频率学有效性：高阶渐近分析AI 解读

Given a random sample from a distribution with density function that depends on an unknown parameter θ = (θ1, θ2), we are concerned with frequentist validity, up to o(n−1), of posterior quantiles of θ1, treating θ2 as a nuisance parameter. We propose to make the best choice of the prior on θ by matching, as far as practicable, the posterior and frequentist coverage probabilities up to o(n−1).

效力曲线形状受先验约束的非参数贝叶斯生物测定AI 解读

We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

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动态层级模型AI 解读

SUMMARY An analysis of a time series of cross-sectional data is considered under a Bayesian perspective. Information is modelled in terms of prior distributions and stratified parametric linear models developed by Lindley and Smith and dynamic linear models developed by Harrison and Stevens are merged into a general framework. This is shown to include many models proposed in econometrics and experimental design. Properties of the model are derived and shrinkage estimators…

移动平均参数估计：经典估计的堆积现象与贝叶斯后验AI 解读

The authors analyze posterior distributions of the moving average parameter in the first-order case and sampling distributions of the corresponding maximum likelihood estimator. Sampling distributions 'pile up' at unity when the true parameter is near unity; hence, if one were to difference such a process, estimates of the moving average component of the resulting series would spuriously tend to indicate that the process was overdifferenced. Flat-prior posterior…

利用后验赔率检测多个方差变点AI 解读

This article uses a Bayesian procedure based on obtaining posterior odds to assess the evidence about the existence of multiple changes of variance in a time series. The approach is developed for sequences of independent observations. An extension to consider autoregressive models is also discussed. The information on the data about the location of the change points and the magnitude of the variances at the different pieces of the series is summarized through posterior…

非参数回归中贝叶斯推断的分析AI 解读

The observation model $y_i = \beta(i/n) + \varepsilon_i, 1 \leq i \leq n$, is considered, where the $\varepsilon$'s are i.i.d. with mean zero and variance $\sigma^2$ and $\beta$ is an unknown smooth function. A Gaussian prior distribution is specified by assuming $\beta$ is the solution of a high order stochastic differential equation. The estimation error $\delta = \beta - \hat{\beta}$ is analyzed, where $\hat{\beta}$ is the posterior expectation of $\beta$. Asymptotic…

等变性与复合决策问题AI 解读

This paper obtains some extensions of Gilliland and Hannan's results on equivariance and the compound decision problem. Consider a compound decision problem with restricted component risk and component distributions in a norm compact set of mutually absolutely continuous probability measures. Then the method of proof of a theorem of Gilliland and Hannan translates the results of Mashayekhi on symmetrization of product measures into uniform convergence to zero of the excess…

参数比较的贝叶斯与经验贝叶斯方法AI 解读

The number of successes out of the total number of trials is observed for each of a set of N independent binomial experiment's and the associated success probabilities are compared. Ranking procedures for comparing these success probabilities are constructed under circumstances where the number of trials for each of the experiments may differ by a large amount. A loss function is constructed that represents an appropriate measure of distance between a given ranking of the…

二元与多类别响应数据的贝叶斯分析AI 解读

A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are…

相对效力的收缩估计量AI 解读

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all…

项目反应理论：参数估计技术AI 解读

The Item Characteristic Curve: Dichotomous Response Estimating the Parameters of an Item Characteristic Curve Maximum Likelihood Estimation of Examinee Ability Maximum Likelihood Procedures for Estimating Both Ability and Item Parameters The Rasch Model Marginal Maximum Likelihood Estimation and an EM Algorithm Bayesian Parameter Estimation Procedures The Graded Item Response Nominally Scored Items Markov Chain Monte Carlo Methods Parameter Estimation with Multiple Groups…

参数比较的贝叶斯与经验贝叶斯程序AI 解读

The number of successes out of the total number of trials is observed for each of a set of N independent binomial experiment's and the associated success probabilities are compared. Ranking procedures for comparing these success probabilities are constructed under circumstances where the number of trials for each of the experiments may differ by a large amount. A loss function is constructed that represents an appropriate measure of distance between a given ranking of the…

相对效力的收缩估计量AI 解读

This article examines the finite and infinite sample properties of the shrinkage estimator, motivated by a Bayesian argument, for the log relative potency, proposed in an earlier paper by Kim, Carter, and Hubert. This estimator can be written in closed form and is shown to have finite mean and finite variance in finite samples. As a consequence, this shrinkage estimator has finite frequentist risk, which is an improvement over the usual maximum likelihood estimator, for all…

部分可交换性与调查抽样推断AI 解读

The role of the sampling mechanism for Bayesian inference on symmetric functions of a finite population is examined under partial design and partial label information. A new definition of partial exchangeability is proposed, together with a corresponding property of the sampling mechanism. These properties provide conditions under which certain symmetries in priors or designs can protect against lack of symmetry in others, in the sense of Scott & Smith (1973).

利用参考先验消除干扰参数AI 解读

The problem of eliminating nuisance parameters is tackled from different points of view. Standard likelihood techniques, such as profile likelihood and its modifications, are compared with a Bayesian analysis based on reference priors (Berger & Bernardo, 1992a). Examples are considered to illustrate what happens in multiparameter problems. In particular the frequentist coverage probabilities of the credible sets derived from the reference priors are shown to be better than…

球对称模型中的稳健贝叶斯推断AI 解读

The class of multivariate I4-spherical di,tributions is introduced and defined through their isodensity surfaces.We prove that, under a JeHreys' type improper prior on the scale parameter, posterior inference on the location parameters is the same for all Iq-spherical sampling models with common q.7itis gives us perfect inference robustness with respect to any departures from the reference case of independcnt sampling from the exponential power distribution.

稳态学习与纳什均衡AI 解读

The authors study the steady states of a system in which players learn about the strategies their opponents are playing by updating their Bayesian priors in light of their observations. Players are matched.at random to play a fixed extensive-form game and each player observes the realized actions in his own matches but not the intended off-path play of his opponents or the realized actions in other matches. Because players are assumed to live finite lives, there are steady…

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有限因变量模型的贝叶斯推断：罢工持续时间应用AI 解读

Abstract This paper presents a straightforward set of Bayesian techniques for analyzing models involving limited dependent variables; the techniques are demonstrated in an analysis of Kennan's (1985) data on contract strikes in US manufacturing. The data are analyzed by deriving posterior distributions—including probability distributions—of hazard functions for strike duration using numerical Monte Carlo methods. The distributions are employed to derive coverage intervals…

删失数据的贝叶斯自助法AI 解读

A Bayesian bootstrap for a censored data model is introduced. Its small sample distributional properties are discussed and found to be similar to Efron's bootstrap for censored data. In the absence of censoring, the Bayesian bootstrap for censored data reduces to Rubin's Bayesian bootstrap for complete data. A first-order large-sample theory is developed. This theory shows that both censored data bootstraps are consistent bootstraps for approximating the sampling…